0. Functions

Determine if the function is an exponential function.  

If so, identify the power & base, then evaluate for $x=4$.

$f\(\left\)(x\(\right\))=\(\left\)(-2\(\right\))^{x}$

Can a function be both even and odd? Give reasons for your answer.

Find the inverse $f^{-1}\(\left\)(x\(\right\))$ of each function (on the given interval, if specified).

$f\(\left\)(x\(\right\))=\(\frac{2}{x^2+1}\)$, for $x\(\geq{0}\)$

Find the domain of the rational function. Then, write it in lowest terms.

$f\(\left\)(x\(\right\))=\(\frac{x^2+9}{x-3}\)$

Finding a Viewing Window

In Exercises 5–30, find an appropriate graphing software viewing window for the given function and use it to display that function’s graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function.

f(x) = (x² − 1)/(x² + 1)

In Exercises 67–72, you will explore some functions and their inverses together with their derivatives and tangent line approximations at specified points. Perform the following steps using your CAS:

b. Solve the equation y=f(x) for x as a function of y, and name the resulting inverse function g.

67. y= √(3x-2), 2/3 ≤ x ≤ 4, x_0=3

Solving trigonometric equations Solve the following equations.

tan x = 1

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.

d. At what time is the ball at a height of 30 ft on the way up?

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.

b. Find the inverse function that gives the time t at which the ball is at height h as the ball travels upward. Express your answer in the form t = ƒ⁻¹ (h)

Solving trigonometric equations Solve the following equations.

sin²Θ = 1/4 , 0 ≤ Θ < 2π

Splitting up curves The unit circle x² + y² = 1  consists of four one-to-one functions, ƒ₁ (x), ƒ₂(x) , ƒ₃(x), and ƒ₄ (x)  (see figure)<IMAGE>.

b. Find the inverse of each function and write it as y= ƒ⁻¹ (x)

Even and Odd Functions

In Exercises 47–62, say whether the function is even, odd, or neither. Give reasons for your answer.

f(x) = x⁻⁵

{Use of Tech} Launching a rocket A small rocket is launched vertically upward from the edge of a cliff $80$ ft above the ground at a speed of $96$ ft/s. Its height (in feet) above the ground is given by $h\(\left\)(t\(\right\))=-16t^2+96t+80$, where $t$ represents time measured in seconds.

a. Assuming the rocket is launched at $t=0$, what is an appropriate domain for $h$?

Determine whether the following statements are true and give an explanation or counterexample.

If y= 3ˣ , then x = ³√y

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph the upper branch of the hyperbola y² − 16x² = 1.