0. Functions

Determine if the function is an exponential function.  

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

$f\left(x\right)=\left(\frac12\right)^{x}$

Even and odd at the origin

a. If ƒ(0) is defined and ƒ is an even function, is it necessarily true that ƒ(0) = 0? Explain.

{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.

a. Is this function one-to-one on the interval 0 ≤ t ≤ 4?

{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)

{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.

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

{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.

e. At what time is the ball at a height of 10 ft on the way down? 

Find the linear function whose graph passes through the point (3, 2) and is parallel to the line $y=3x+8$ .

Solve the equation sin 2Θ = 1, for 0 ≤ Θ < 2π .

Evaluate cos⁻¹(cos(5π/4)).

Solving trigonometric equations Solve the following equations.

tan x = 1

Solving trigonometric equations Solve the following equations.

cos²Θ = 1/2 , 0 ≤ Θ < 2π

Solving trigonometric equations Solve the following equations.

sin Θ cos Θ = 0, 0 ≤ Θ < 2π

Solving trigonometric equations Solve the following equations.

sin²Θ = 1/4 , 0 ≤ Θ < 2π

Area of a circular sector Prove that the area of a sector of a circle of radius r associated with a central angle $\theta$ (measured in radians) is $A=\frac12r^2\theta$.

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