Exam 1: Functions and Their Graphs

$For the function, find the average rate of change of f from 1 to x: \frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1 - f ( x ) = x ^ { 3 } + x$ For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = x ^ { 3 } + x$

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Question 1

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Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f ( x ) = \sqrt { x } + 1$ $Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f ( x ) = \sqrt { x } + 1$

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Question 2

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The graph of a function f is given. Use the graph to answer the question. -How often does the line y = -10 intersect the graph?

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Question 3

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Determine algebraically whether the function is even, odd, or neither. - $\sqrt [ 3 ] { 5 x ^ { 2 } + 4 }$

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Question 4

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$

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Question 5

$For the function, find the average rate of change of f from 1 to x: \frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1 - f ( x ) = \sqrt { x + 63 }$ For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \sqrt { x + 63 }$

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Question 6

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(10).

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Question 7

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 2, 0)

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Question 8

The graph of a piecewise-defined function is given. Write a definition for the function. -

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Question 9

Solve the problem. -A gas company has the following rate schedule for natural gas usage in single-family residences: What is the charge for using 25 therms in one month? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas.

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Question 10

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \frac { 2 } { x + 1 }$

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Question 11

Answer the question about the given function. -Given the functi $f ( x ) = - 6 x ^ { 2 } - 12 x + 5$ , what is the domain of f?

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Question 12

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

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Question 13

Determine whether the equation defines y as a function of x. -y = x²

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Question 14

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\sqrt{x+4}+2$ $Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=\sqrt{x+4}+2$

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Question 15

Solve the problem. -If a rock falls from a height of 40 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 40 - 4.9 x ^ { 2 }$ When does the rock strike the ground? Round to the nearest hundredth, if necessary.

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Question 16

Solve. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 15 minutes requires 7.5 gallons of water. Find the amount of water used in a shower Lasting 8 minutes.

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Question 17

Solve. -The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 4 hours and uses 28 gallons of fuel. Find the number of gallons of fuel that the helicopter uses To fly for 6 hours.

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Question 18

Solve the problem. -If a rock falls from a height of 30 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 30 - 4.9 x ^ { 2 }$ What is the height of the rock when x = 1.9 seconds? Round to the nearest hundredth, if necessary.

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Question 19

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$ Find $f \cdot g$ .

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Question 20

Showing 1 - 20 of 276

$For the function, find the average rate of change of f from 1 to x: \frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1 - f ( x ) = x ^ { 3 } + x$ For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = x ^ { 3 } + x$

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = -10 intersect the graph?

Determine algebraically whether the function is even, odd, or neither. - $\sqrt [ 3 ] { 5 x ^ { 2 } + 4 }$

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$

$For the function, find the average rate of change of f from 1 to x: \frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1 - f ( x ) = \sqrt { x + 63 }$ For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \sqrt { x + 63 }$

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(10).

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 2, 0)

The graph of a piecewise-defined function is given. Write a definition for the function. -

Solve the problem. -A gas company has the following rate schedule for natural gas usage in single-family residences: What is the charge for using 25 therms in one month? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas.

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \frac { 2 } { x + 1 }$

Answer the question about the given function. -Given the functi $f ( x ) = - 6 x ^ { 2 } - 12 x + 5$ , what is the domain of f?

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Determine whether the equation defines y as a function of x. -y = x²

Solve the problem. -If a rock falls from a height of 40 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 40 - 4.9 x ^ { 2 }$ When does the rock strike the ground? Round to the nearest hundredth, if necessary.

Solve. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 15 minutes requires 7.5 gallons of water. Find the amount of water used in a shower Lasting 8 minutes.

Solve. -The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 4 hours and uses 28 gallons of fuel. Find the number of gallons of fuel that the helicopter uses To fly for 6 hours.

Solve the problem. -If a rock falls from a height of 30 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 30 - 4.9 x ^ { 2 }$ What is the height of the rock when x = 1.9 seconds? Round to the nearest hundredth, if necessary.

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$ Find $f \cdot g$ .

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Exam 1: Functions and Their Graphs

For the function, find the average rate of change of f from 1 to x: f(x)−f(1)x−1,x≠1\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1x−1f(x)−f(1)​,x=1 - f(x)=x3+xf ( x ) = x ^ { 3 } + xf(x)=x3+x

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=x+1f ( x ) = \sqrt { x } + 1f(x)=x​+1

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = -10 intersect the graph?

Determine algebraically whether the function is even, odd, or neither. - 5x2+43\sqrt [ 3 ] { 5 x ^ { 2 } + 4 }35x2+4​

Graph the function. - f(x)=x3f ( x ) = \sqrt [ 3 ] { x }f(x)=3x​

For the function, find the average rate of change of f from 1 to x: f(x)−f(1)x−1,x≠1\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1x−1f(x)−f(1)​,x=1 - f(x)=x+63f ( x ) = \sqrt { x + 63 }f(x)=x+63​

The graph of a function f is given. Use the graph to answer the question. -Use the graph of f given below to find f(10).

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(- 2, 0)

The graph of a piecewise-defined function is given. Write a definition for the function. -

Solve the problem. -A gas company has the following rate schedule for natural gas usage in single-family residences: What is the charge for using 25 therms in one month? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas.

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - f(x)=2x+1f ( x ) = \frac { 2 } { x + 1 }f(x)=x+12​

Answer the question about the given function. -Given the functi f(x)=−6x2−12x+5f ( x ) = - 6 x ^ { 2 } - 12 x + 5f(x)=−6x2−12x+5 , what is the domain of f?

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Determine whether the equation defines y as a function of x. -y = x2

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=x+4+2f(x)=\sqrt{x+4}+2f(x)=x+4​+2

Solve the problem. -If a rock falls from a height of 40 meters on Earth, the height H (in meters) after x seconds is approximately H(x)=40−4.9x2H ( x ) = 40 - 4.9 x ^ { 2 }H(x)=40−4.9x2 When does the rock strike the ground? Round to the nearest hundredth, if necessary.

Solve. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 15 minutes requires 7.5 gallons of water. Find the amount of water used in a shower Lasting 8 minutes.

Solve. -The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 4 hours and uses 28 gallons of fuel. Find the number of gallons of fuel that the helicopter uses To fly for 6 hours.

Solve the problem. -If a rock falls from a height of 30 meters on Earth, the height H (in meters) after x seconds is approximately H(x)=30−4.9x2H ( x ) = 30 - 4.9 x ^ { 2 }H(x)=30−4.9x2 What is the height of the rock when x = 1.9 seconds? Round to the nearest hundredth, if necessary.

For the given functions f and g, find the requested function and state its domain. - f(x)=7−x;g(x)=x−3f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }f(x)=7−x​;g(x)=x−3​ Find f⋅gf \cdot gf⋅g .

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

$For the function, find the average rate of change of f from 1 to x: \frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1 - f ( x ) = x ^ { 3 } + x$ For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = x ^ { 3 } + x$

Determine algebraically whether the function is even, odd, or neither. - $\sqrt [ 3 ] { 5 x ^ { 2 } + 4 }$

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$

$For the function, find the average rate of change of f from 1 to x: \frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1 - f ( x ) = \sqrt { x + 63 }$ For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \sqrt { x + 63 }$

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = \frac { 2 } { x + 1 }$

Answer the question about the given function. -Given the functi $f ( x ) = - 6 x ^ { 2 } - 12 x + 5$ , what is the domain of f?

Determine whether the equation defines y as a function of x. -y = x²

Solve the problem. -If a rock falls from a height of 40 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 40 - 4.9 x ^ { 2 }$ When does the rock strike the ground? Round to the nearest hundredth, if necessary.

Solve the problem. -If a rock falls from a height of 30 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 30 - 4.9 x ^ { 2 }$ What is the height of the rock when x = 1.9 seconds? Round to the nearest hundredth, if necessary.

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$ Find $f \cdot g$ .