Exam 1: Functions and Limits

When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by $Q(t)=Q_{0}\left(1-e^{-t / a}\right)$ (The maximum charge capacity $Q_{0}$ is and t is measured in seconds.) How long does it take to recharge the capacitor to 90% of capacity if $a=5$ ?

Find an expression for the function $y=f(x)$ whose graph is the bottom half of the parabola $x+(6-y)^{2}=0$ .

Under ideal conditions a certain bacteria population is known to double every three hours. Suppose that there are initially 45 bacteria. What is the size of the population after 15 hours?

Find the domain of the function. $f(x)=\frac{1}{3 x-1}$

Find all solutions of the equation correct to two decimal places. $\tan x=\sqrt{1-x^{2}}$

Plot the graph of the function in (a) the standard viewing window and (b) the indicated window. f (x) = x $\sqrt{7-x^{4}}$ , [-3, 3] × [-5, 5]

Fill in the blanks. Let $f(x)=5+x^{2}+\tan \left(\frac{\pi x}{2}\right)$ , where $-1<$$x< 1$ . $f^{-1}(5)=$ __________ $f\left(f^{-1}(6)\right)=$ __________

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. $F=\frac{9}{5} C+32$ What is the F-intercept and what does it represent?

Find the range of the function. $h(x)=\sqrt{4-x^{2}}$

What is the equation of this graph?

Find the exact value of the expression. $\cos \left(\arcsin \frac{1}{2}\right)$

For what values of x is the inequality $|\sin x-x|<0.5$ true? Write your answer correct to two decimal places.

Plot the graph of the function f in an appropriate viewing window. $f(x)=\frac{x^{4}}{x^{4}+3}$

Which of the following is the equation for the function $g(x)$ ?

Find the zero(s) of the function f to five decimal places. f (x) = $x^{3}$ - 5x + 1