Exam 1: Functions and Graphs

Angela drives on a county highway for 2 hours. She travels 112 miles during this time. She averages 22 mph faster on this drive than she does in the city traffic. What is her average speed in the city?

A ball is hit straight up from a height of 3 ft with an initial velocity of 60 ft/sec . Write a set of parametric equations that you would use to graph height against time. Then find the maximum height of the ball and the number of seconds to reach that height.

Write the equation whose graph can be obtained from the graph of $y=x^{2}$ by a vertical stretching of factor 4 , a reflection through the x -axis, and a vertical shift 5 units up.

Three of the twelve basic functions are even functions. Which are they?

(a) Graph the piecewise function $f(x)=\left\{\begin{array}{l}x^{2}+4, \text { if } x \leq 0 \\3 x-5, \text { if } x>0\end{array}\right\} .$ (b) Is the function continuous? Why or why not?

Solve the inequality $|3 x+6| \geq 1$ algebraically. Write the solution in interval notation and draw its number line graph.

Let $f(x)=3 x^{2}-5$ and $g(x)=\frac{2}{x} \text {. }$ Find the function $f \circ g$ Give the domain of $f \circ g .$

(a) Graph the piecewise function $f(x)=\left\{\begin{array}{ll}x^{3}+2, & \text { if } x>0 \\2-x, & \text { if } x<0\end{array}\right\} .$ (b) Is the function continuous? Why or why not?

Find the range of the function $f(x)=x^{3}+\sqrt{x-2}$ Give your answer in interval notation.

Solve the equation $-x^{2}-x+12=0$ Give exact solutions.

Describe how the graph of $f(x)=x^{4}-2$ can be transformed to the graph of $g(x)=(2 x)^{4}-2$

Describe how the graph of $y=(2 x+2)^{2}$ can be obtained from the graph of $y=x^{2}$

A ball is hit straight up from a height of 4 ft with an initial velocity of 65 ft/sec. Write a set of parametric equations that you would use to graph height against time. Then find the maximum height of the ball and the number of seconds to reach that height.

Determine the domain of the real-valued function f(x)=ln (x-4) .

The graph of which of the following functions is bounded above by x=2?

-The graph above is a slight variation of one of the ten basic functions. Which of the following equations best represents the graph?

Alfred receives a salary of $2500 per month, and he pays $550 per month in rent. What percentage of his salary is spent on rent?

Find the inverse relation of $f(x)=\frac{6 x+5}{3 x-1}$

Graph the relation defined by the parametric equations below. Use an appropriate window size for $-3 \leq t \leq 3$ . $x=3-t^{2}, y=1+2 t$

Graph the relation defined by the parametric equations $x=2 t^{2}-4$ and $y=2 t$ . Use a $[-5,5]$ by $[-5,5]$ viewing window and $-2 t 2$ .