Precalculus - Chapter 1 Review

Not a Function

Function or Not?

lim x→∞, = -∞,

lim x→-∞ = ∞

Describe the end behavior of g(x) = -4x³-5x+1

(-∞, -4)U[10, ∞)

Describe the set of numbers below using interval notation:

x

(-1.45, -6.76)

Determine the relative minimum point of the following function:

f(x) = -2x³-4x² + x - 3

(0.12, -2.94)

Determine the relative maximum point of the following function:

f(x) = -2x³-4x² + x - 3

-3x² + 4x - 12

Given that f(x) = -7 - 2x² and g(x) = 5 - 4x + x², find (f - g)(x)

-2x² + 20x - 47

Given that f(x) = 3 - 2x² and g(x) = 5 - x, find (f ° g)(x)

Reflection over the x-axis, left 3 units, down 1 unit

Given the parent function f(x) = x², describe the following transformation g(x):

g(x) = -(x + 3)² - 1

Vertical stretch by a factor of 2, reflection over the y-axis, up 3 units

Given the parent function f(x) = √x, describe the following transformation g(x):

g(x) = 2√-x + 3

[-2, 10)

Describe the set of numbers below using interval notation:

-2 ≤ x < 10

51 feet

A football is launched in the air and can be modeled by the equation h(t) = -16t² + 48t + 15 where t is in seconds and h is in feet. How high did the football reach?

1.5 seconds

A football is launched in the air and can be modeled by the equation h(t) = -16t² + 48t + 15 where t is in seconds and h is in feet. When does the football reach its maximum height?

3.29 seconds

A football is launched in the air and can be modeled by the equation h(t) = -16t² + 48t + 15 where t is in seconds and h is in feet. When does the football hit the ground?

1

Given that g(x) = 5 - 6x - 4x², find f(-2)

-½x + 2

Given that f(x) = -2x + 4, find f⁻¹(x)

2

Given that f(x) = 3 - 2x² and g(x) = 5 - 3x, find (g ° f)(-1)

-9

Find the average rate of change of f(x) = -2x² - 3x + 4 on [-1, 4]

y = √(x + 2)+1

Identify the equation that will produce the related function shown in blue if the parent function f(x) = √x is shown in red.

(-1.45, 0.12)

Determine the intervals for which f(x) is increasing:

f(x) = -2x³-4x² + x - 3

(-∞, -1.45)U(0.12, ∞)

Determine the intervals for which f(x) is decreasing:

f(x) = -2x³-4x² + x - 3