Exam 2: Functions and Graphs

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. ​ ​

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. ​ x-y=10 3x-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 ​

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.