Functions and Mathematical Models Online Quiz Questions

What is the domain of the function g(x) = √(x + 5)?

Relative to the parent function y = √x, what translations occur in y = √(2x - 6) + 1?

For y = 3 cos(2x - π/2) + 1, which pair gives the amplitude and period?

Select all statements that are necessarily true for a function.

Select all statements that describe valid ways a function's domain can be restricted.

True or false: In (f ∘ g)(x), the function g acts first and the function f acts second.

True or false: The function f(x) = x² has an inverse function on all of the real numbers.

In the function y = √(2x - 6) + 1, enter the magnitude of the horizontal shift in units. Do not include the direction word; the direction is to the right.

Let f(x) = x² + 1 and g(x) = 3x - 2. Compute (f ∘ g)(x) and (g ∘ f)(x), and explain why the two results demonstrate that function composition is generally not commutative.

For f(x) = 2x + 3, enter the value of f(4) as a whole number.

A particle has position s(t) = t³ - 6t² + 9t for 0 ≤ t ≤ 4. Its velocity is v(t) = 3(t - 1)(t - 3). On which intervals is the particle's position increasing and decreasing?

True or false: In calculus, trigonometric derivatives are conventionally expressed using radian measure.

Let f(x) = x² + 1 and g(x) = 3x - 2. Which expression represents (f ∘ g)(x)?

In the continuous model P(t) = P₀e^(kt), what does k = -0.08 indicate?

Relative to y = f(x), what are the horizontal and vertical effects of y = 2f(x - 3) + 1?

For y = 4 sin(3x), what is the period in radians? Give a decimal answer within 0.001.

If f(x) = 2x - 5, which formula is f⁻¹(x)?

A population is modeled by $P(t)=200\cdot 2^t$, where $t$ is measured in years. After how many years will the population reach 1,600? Enter the value in years. The absolute tolerance is 0 years.