Exam 1: Functions and Their Graphs

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\frac{7}{x}$ $Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=\frac{7}{x}$

(Multiple Choice)

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Question 41

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$ Find $\frac { f } { g }$ .

(Multiple Choice)

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Question 42

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { x } { x ^ { 2 } + 5 }$

(Multiple Choice)

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Question 43

Find the value for the function. -Find $f ( x + h )$ when $f ( x ) = \frac { 9 x + 8 } { 8 x - 3 }$ .

(Multiple Choice)

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Question 44

The graph of a function f is given. Use the graph to answer the question. -Is f(8) positive or negative?

(Multiple Choice)

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Question 45

The graph of a function f is given. Use the graph to answer the question. -For what numbers $x$ is $f ( x ) > 0$ ?

(Multiple Choice)

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Question 46

Solve the problem. -If f(x) = int(4x), find f(1.8).

(Multiple Choice)

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Question 47

The graph of a function is given. Decide whether it is even, odd, or neither. -

(Multiple Choice)

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Question 48

Find the domain of the function. - $f(x)=\left\{\begin{array}{ll}1 & \text { if }-9 \leq x<-3 \\|x| & \text { if }-3 \leq x<9 \\\sqrt[3]{x} & \text { if } 9 \leq x \leq 33\end{array}\right.$

(Multiple Choice)

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Question 49

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

(Multiple Choice)

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Question 50

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local minimum. What are the local minima?

(Multiple Choice)

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Question 51

Find the value for the function. -Find $f ( 0 )$ when $f ( x ) = \sqrt { x ^ { 2 } + 2 x }$

(Multiple Choice)

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Question 52

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\sqrt{x-4}-3$ $Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=\sqrt{x-4}-3$

(Multiple Choice)

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Question 53

Solve the problem. -If $f ( x ) = \frac { x - 4 A } { - 12 x + 3 }$ and $f ( - 12 ) = - 4$ , what is the value of $A ?$

(Multiple Choice)

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Question 54

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local maximum. What are the local maxima?

(Multiple Choice)

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Question 55

Determine whether the equation defines y as a function of x. - $x = y ^ { 2 }$

(Multiple Choice)

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Question 56

Determine whether the equation defines y as a function of x. - $y = x ^ { 4 }$

(Multiple Choice)

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Question 57

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7$

(Multiple Choice)

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Question 58

Determine algebraically whether the function is even, odd, or neither. - $\sqrt [ 3 ] { 7 x ^ { 2 } + 4 }$

(Multiple Choice)

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Question 59

Find the value for the function. -Find $f ( - 2 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x - 1 }$

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Question 60

Showing 41 - 60 of 297

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$ Find $\frac { f } { g }$ .

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { x } { x ^ { 2 } + 5 }$

Find the value for the function. -Find $f ( x + h )$ when $f ( x ) = \frac { 9 x + 8 } { 8 x - 3 }$ .

The graph of a function f is given. Use the graph to answer the question. -Is f(8) positive or negative?

The graph of a function f is given. Use the graph to answer the question. -For what numbers $x$ is $f ( x ) > 0$ ?

Solve the problem. -If f(x) = int(4x), find f(1.8).

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the domain of the function. - $f(x)=\left\{\begin{array}{ll}1 & \text { if }-9 \leq x<-3 \\|x| & \text { if }-3 \leq x<9 \\\sqrt[3]{x} & \text { if } 9 \leq x \leq 33\end{array}\right.$

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

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local minimum. What are the local minima?

Find the value for the function. -Find $f ( 0 )$ when $f ( x ) = \sqrt { x ^ { 2 } + 2 x }$

Solve the problem. -If $f ( x ) = \frac { x - 4 A } { - 12 x + 3 }$ and $f ( - 12 ) = - 4$ , what is the value of $A ?$

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local maximum. What are the local maxima?

Determine whether the equation defines y as a function of x. - $x = y ^ { 2 }$

Determine whether the equation defines y as a function of x. - $y = x ^ { 4 }$

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7$

Determine algebraically whether the function is even, odd, or neither. - $\sqrt [ 3 ] { 7 x ^ { 2 } + 4 }$

Find the value for the function. -Find $f ( - 2 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x - 1 }$

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 1: Functions and Their Graphs

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)=7xf(x)=\frac{7}{x}f(x)=x7​

For the given functions f and g, find the requested function and state its domain. - f(x)=x;g(x)=5x−2f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2f(x)=x​;g(x)=5x−2 Find fg\frac { f } { g }gf​ .

Determine algebraically whether the function is even, odd, or neither. - f(x)=xx2+5f ( x ) = \frac { x } { x ^ { 2 } + 5 }f(x)=x2+5x​

Find the value for the function. -Find f(x+h)f ( x + h )f(x+h) when f(x)=9x+88x−3f ( x ) = \frac { 9 x + 8 } { 8 x - 3 }f(x)=8x−39x+8​ .

The graph of a function f is given. Use the graph to answer the question. -Is f(8) positive or negative?

The graph of a function f is given. Use the graph to answer the question. -For what numbers xxx is f(x)>0f ( x ) > 0f(x)>0 ?

Solve the problem. -If f(x) = int(4x), find f(1.8).

The graph of a function is given. Decide whether it is even, odd, or neither. -

Graph the function. - f(x)=xf ( x ) = \sqrt { x }f(x)=x​

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local minimum. What are the local minima?

Find the value for the function. -Find f(0)f ( 0 )f(0) when f(x)=x2+2xf ( x ) = \sqrt { x ^ { 2 } + 2 x }f(x)=x2+2x​

Choose the one alternative that best completes the statement or answers the question. 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−4−3f(x)=\sqrt{x-4}-3f(x)=x−4​−3

Solve the problem. -If f(x)=x−4A−12x+3f ( x ) = \frac { x - 4 A } { - 12 x + 3 }f(x)=−12x+3x−4A​ and f(−12)=−4f ( - 12 ) = - 4f(−12)=−4 , what is the value of A?A ?A?

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local maximum. What are the local maxima?

Determine whether the equation defines y as a function of x. - x=y2x = y ^ { 2 }x=y2

Determine whether the equation defines y as a function of x. - y=x4y = x ^ { 4 }y=x4

Find the average rate of change for the function between the given values. - f(x)=3x−2; from 4 to 7f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7f(x)=x−23​; from 4 to 7

Determine algebraically whether the function is even, odd, or neither. - 7x2+43\sqrt [ 3 ] { 7 x ^ { 2 } + 4 }37x2+4​

Find the value for the function. -Find f(−2)f ( - 2 )f(−2) when f(x)=x2−7x−1f ( x ) = \frac { x ^ { 2 } - 7 } { x - 1 }f(x)=x−1x2−7​

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x } ; g ( x ) = 5 x - 2$ Find $\frac { f } { g }$ .

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { x } { x ^ { 2 } + 5 }$

Find the value for the function. -Find $f ( x + h )$ when $f ( x ) = \frac { 9 x + 8 } { 8 x - 3 }$ .

The graph of a function f is given. Use the graph to answer the question. -For what numbers $x$ is $f ( x ) > 0$ ?

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

Find the value for the function. -Find $f ( 0 )$ when $f ( x ) = \sqrt { x ^ { 2 } + 2 x }$

Solve the problem. -If $f ( x ) = \frac { x - 4 A } { - 12 x + 3 }$ and $f ( - 12 ) = - 4$ , what is the value of $A ?$

Determine whether the equation defines y as a function of x. - $x = y ^ { 2 }$

Determine whether the equation defines y as a function of x. - $y = x ^ { 4 }$

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7$

Determine algebraically whether the function is even, odd, or neither. - $\sqrt [ 3 ] { 7 x ^ { 2 } + 4 }$

Find the value for the function. -Find $f ( - 2 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x - 1 }$