Deck 2: Functions and Graphs

Question 1

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.
​ ​ $$a = 5 , b = 7$$ ​

Answer 1

$\Theta \approx 35.5 ^ { \circ }$

Question 2

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

Answer 2

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Question 3

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

Answer 3

Symmetric with respect to the x-axis.

Question 4

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.
​ $\begin{array} { l } x - y = 10 \\3 x - 2 y = 1\end{array}$ ​

Question 5

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

Question 6

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

Question 7

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.
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Question 8

Find the distance between the point and the line. Round your answer to four decimal places. $$\begin{array}{ll}\text {Point }&\text {Line }\\(5,6)&7 x+y=1\end{array}$$
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Question 9

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

Question 10

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

Question 11

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.
​
x > 3 and y < 0
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Question 12

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.

Question 13

Evaluate $g ( s + 10 )$ if $g ( y ) = 11 - 4 y$ .
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Question 14

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