Exam 2: Functions

Find a formula for the following graph:

Write a formula for the following function:

Assume that height is a function of age and that $H=f(a)$ is the average height (in inches) for females in the US at age $a$ years. What is a reasonable domain for $H=f(a)$ ?

An organization has 175 raffle tickets to sell for $\$ 5$ each. From the proceeds of the sale, they will award the winning ticket holder $\$ 100$ . The profit, $P$ , that the organization receives is a function of the number, $n$ , of tickets sold. Assuming they sell at least one ticket, the range of this function is ------------- $\leq$ ------------ $\leq$ -----------.

The number of bacteria in a sample grows slowly at first, but then grows with increasing rapidity. Does the following figure accurately represent the number of bacteria in a sample graphed against time?

Let $f(x)=\frac{7}{(x-3)^{2}}$ . a) Graph $f(x)$ . b) Use the graph to find the range of the function on the domain $[-2,4]$ .

If $f(x)$ is decreasing and concave down on $-10<x<10$ , which of the following must be true.

Use the table below to answer the following questions. If $g(x)=f(x-1)-8$ , compute A) $g(-1)$ B) $g(0)$ C) $g(1)$

Given the function $f(x)=5 x-2$ , find the domain of $f^{-1}(x)$ .

The data points for the following table are graphed in the figures below. For the graph that is a function, we could write -----------=f(----------------), where is ------------ the dependent variable and ----------------- is the independent variable. (Fill in each blank with an $" s "$ or a " $t$ ").

If $y=f(x)=x^{7}+6$ , what is the inverse function $f^{-1}(y)$ ?

The data points for the following table are graphed in the figure below. For the graph that is a function, approximate $f(-0.5)$ .

The function $D(p)=1200-200 p$ gives the weekly demand for DVD rentals at Joe's Videolog when Joe charges $\$ p$ to rent a DVD. What does $D^{-1}(60)$ mean in practical terms?

If $f$ is increasing on $1<x<19$ , then $f(3)>f(16)$

Let $I(x)$ be the federal income tax paid based on a total taxable income of $x$ dollars. The value of $I(x)$ is approximated by the graph in the following figure. Which of the following would represent a decrease in your income tax if your income was $w$ dollars?

Use the following table to evaluate $f(2)$ .

Let $y=p(x)$ be defined by the following graph, and let $y_{0}=p\left(x_{0}\right)$ and $y_{1}=p\left(x_{1}\right)$ . Which of the following two values is greater?

If $f(x)=\frac{1}{x+5}+2$ , solve $f(x)=0$ for $x$ . Rounded to 2 decimal places.