Question 1

A rectangle is bounded by the x-axis and the semicircle $y = \sqrt { 49 - x ^ { 2 } }$ (see figure). Select the area A of the rectangle as a function of x, and determine the domain of the function.
​  ​

Accepted Answer

$$A ( x ) = 2 | x | \sqrt { 49 - x ^ { 2 } }$$ , $- 7 \leq x \leq 7$

Question 2

Find the value(s) of x for which $f ( x ) = g ( x )$ .
​ $f ( x ) = x ^ { 2 } + 4 x - 26$ $g ( x ) = 7 x - 8$ ​

Accepted Answer

x= -3, 6

Question 3

Evaluate $g ( s + 10 )$ if $g ( y ) = 11 - 4 y$ .
​

Accepted Answer

$g ( s + 10 ) = - 29 - 4 s$

Question 4

Select the graph of g.
​ $g ( x ) = 5 ( x - 4 ) ^ { 3 }$ ​

Accepted Answer

The answer of Select the graph of g.
​ \(g (...

Question 5

The parent function $f ( x ) = \sqrt { x }$ is related to g. Describe the sequence of transformations from f to g.
​ $g ( x ) = \sqrt { x - 3 }$ ​

Accepted Answer

The answer of The parent function \(f ( x )...

Question 6

A roof has a rise of 5 feet for every horizontal change of 7 feet (see figure). Find the inclination of the roof. Round your answers to one decimal place.
​  ​ $$a = 5 , b = 7$$ ​

Accepted Answer

The answer of A roof has a rise of 5...

Question 7

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.
​
x > 3 and y < 0
​

Accepted Answer

The answer of Determine the quadrant(s) in which (x, y)...

Question 8

Find the angle $\theta$ (in radians and degrees) between the lines. Round your answer to four decimal places for radians and round your answer to one decimal places for degree.
​ $\begin{array} { l } 
x - y = 10 \
3 x - 2 y = 1
\end{array}$ ​

Accepted Answer

The answer of Find the angle $\theta$ (in radians and...

Question 9

Find the distance between the point and the line. Round your answer to four decimal places. $$\begin{array}{ll}
\text {Point }&\text {Line }\(5,6)&7 x+y=1
\end{array}$$
 ​

Accepted Answer

The answer of Find the distance between the point and...

Question 10

Graphically estimate the x- and y-intercepts of the graph.
​ $$y = 2 - 2 x ^ { 3 }$$ ​  ​

Accepted Answer

The answer of Graphically estimate the x- and y-intercepts of...

Question 11

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } - 4 x - 9$ , determine the equation of the axis of symmetry.

Accepted Answer

The answer of From the graph of the quadratic function...

Question 12

Find the inclination Θ (in degrees) of the line with a slope of m. Round your answer to one decimal places.
​ $m = 0.6666666667$ ​

Accepted Answer

The answer of Find the inclination Θ (in degrees) of...

Question 13

Use algebraic tests to check the following for symmetry with respect to the axes and the origin.
​ $10 x + 4 y ^ { 8 } = 0$ ​

Accepted Answer

The answer of Use algebraic tests to check the following...

Question 14

Write an equation for the function that is described by the following characteristics.
The shape of $f ( x ) = x ^ { 2 }$ , but moved eight units down, two units to the left, and then reflected in the x-axis.

Accepted Answer

The answer of Write an equation for the function that...

Exam 2: Functions and Graphs

Find the value(s) of x for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } + 4 x - 26$ $g ( x ) = 7 x - 8$

Evaluate $g ( s + 10 )$ if $g ( y ) = 11 - 4 y$ .

Select the graph of g. $g ( x ) = 5 ( x - 4 ) ^ { 3 }$

The parent function $f ( x ) = \sqrt { x }$ is related to g. Describe the sequence of transformations from f to g. $g ( x ) = \sqrt { x - 3 }$

A roof has a rise of 5 feet for every horizontal change of 7 feet (see figure). Find the inclination of the roof. Round your answers to one decimal place. $a = 5 , b = 7$

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. x > 3 and y < 0

Find the angle $\theta$ (in radians and degrees) between the lines. Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $\begin{array} { l } x - y = 10 \\3 x - 2 y = 1\end{array}$

Find the distance between the point and the line. Round your answer to four decimal places. $\begin{array}{ll}\text {Point }&\text {Line }\5,6)&7 x+y=1\end{array}$

Graphically estimate the x- and y-intercepts of the graph. $y = 2 - 2 x ^ { 3 }$ $Graphically estimate the x- and y-intercepts of the graph. y = 2 - 2 x ^ { 3 } $

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } - 4 x - 9$ , determine the equation of the axis of symmetry.

Find the inclination Θ (in degrees) of the line with a slope of m. Round your answer to one decimal places. $m = 0.6666666667$

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $10 x + 4 y ^ { 8 } = 0$

Write an equation for the function that is described by the following characteristics. The shape of $f ( x ) = x ^ { 2 }$ , but moved eight units down, two units to the left, and then reflected in the x-axis.

Exam 2: Functions and Graphs

A rectangle is bounded by the x-axis and the semicircle y=49−x2y = \sqrt { 49 - x ^ { 2 } }y=49−x2​ (see figure). Select the area A of the rectangle as a function of x, and determine the domain of the function. ​ ​

Find the value(s) of x for which f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) . ​ f(x)=x2+4x−26f ( x ) = x ^ { 2 } + 4 x - 26f(x)=x2+4x−26 g(x)=7x−8g ( x ) = 7 x - 8g(x)=7x−8 ​

Evaluate g(s+10)g ( s + 10 )g(s+10) if g(y)=11−4yg ( y ) = 11 - 4 yg(y)=11−4y . ​

Select the graph of g. ​ g(x)=5(x−4)3g ( x ) = 5 ( x - 4 ) ^ { 3 }g(x)=5(x−4)3 ​

The parent function f(x)=xf ( x ) = \sqrt { x }f(x)=x​ is related to g. Describe the sequence of transformations from f to g. ​ g(x)=x−3g ( x ) = \sqrt { x - 3 }g(x)=x−3​ ​

A roof has a rise of 5 feet for every horizontal change of 7 feet (see figure). Find the inclination of the roof. Round your answers to one decimal place. ​ ​ a=5,b=7a = 5 , b = 7a=5,b=7 ​

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. ​ x > 3 and y < 0 ​

Find the angle θ\thetaθ (in radians and degrees) between the lines. Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​ x−y=103x−2y=1\begin{array} { l } x - y = 10 \\3 x - 2 y = 1\end{array}x−y=103x−2y=1​ ​

Find the distance between the point and the line. Round your answer to four decimal places. Point Line \5,6)7x+y=1\begin{array}{ll}\text {Point }&\text {Line }\5,6)&7 x+y=1\end{array}Point ​Line \5,6)​7x+y=1​ ​

Graphically estimate the x- and y-intercepts of the graph. ​ y=2−2x3y = 2 - 2 x ^ { 3 }y=2−2x3 ​ ​

From the graph of the quadratic function f(x)=−x2−4x−9f ( x ) = - x ^ { 2 } - 4 x - 9f(x)=−x2−4x−9 , determine the equation of the axis of symmetry.

Find the inclination Θ (in degrees) of the line with a slope of m. Round your answer to one decimal places. ​ m=0.6666666667m = 0.6666666667m=0.6666666667 ​

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. ​ 10x+4y8=010 x + 4 y ^ { 8 } = 010x+4y8=0 ​

Write an equation for the function that is described by the following characteristics. The shape of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 , but moved eight units down, two units to the left, and then reflected in the x-axis.

Find the value(s) of x for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } + 4 x - 26$ $g ( x ) = 7 x - 8$

Evaluate $g ( s + 10 )$ if $g ( y ) = 11 - 4 y$ .

Select the graph of g. $g ( x ) = 5 ( x - 4 ) ^ { 3 }$

The parent function $f ( x ) = \sqrt { x }$ is related to g. Describe the sequence of transformations from f to g. $g ( x ) = \sqrt { x - 3 }$

A roof has a rise of 5 feet for every horizontal change of 7 feet (see figure). Find the inclination of the roof. Round your answers to one decimal place. $a = 5 , b = 7$

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. x > 3 and y < 0

Find the angle $\theta$ (in radians and degrees) between the lines. Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $\begin{array} { l } x - y = 10 \\3 x - 2 y = 1\end{array}$

Find the distance between the point and the line. Round your answer to four decimal places. $\begin{array}{ll}\text {Point }&\text {Line }\5,6)&7 x+y=1\end{array}$

Graphically estimate the x- and y-intercepts of the graph. $y = 2 - 2 x ^ { 3 }$ $Graphically estimate the x- and y-intercepts of the graph. y = 2 - 2 x ^ { 3 } $

From the graph of the quadratic function $f ( x ) = - x ^ { 2 } - 4 x - 9$ , determine the equation of the axis of symmetry.

Find the inclination Θ (in degrees) of the line with a slope of m. Round your answer to one decimal places. $m = 0.6666666667$

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $10 x + 4 y ^ { 8 } = 0$

Write an equation for the function that is described by the following characteristics. The shape of $f ( x ) = x ^ { 2 }$ , but moved eight units down, two units to the left, and then reflected in the x-axis.