Task Sets: Graph exponential, logarithmic, and trigonometric functions - Common Core Math - HS Functions

Concepts

Which statement about the graph of $f(x) = 2^x$ is true?

The graph crosses the $x$ -axis at $(0, 0)$ .

The graph has a horizontal asymptote at $y = 0$ and never goes below it.

The graph eventually crosses the $x$ -axis for large negative $x$ -values.

The range of $f(x) = 2^x$ is all real numbers.

Which equation represents exponential decay?

$f(x) = 3^x$

$f(x) = \left(\tfrac{2}{3}\right)^x$

$f(x) = x^3$

$f(x) = x^2$

What is the x-coordinate of the x-intercept of $f(x) = \log_2(x)$ ?
Enter a number.

What is the y-intercept of $f(x) = 5 \cdot 3^x$ ?
Enter the y-coordinate of the y-intercept.

What is the y-coordinate of the horizontal asymptote of $h(x) = 4 \cdot 2^x - 3$ ?

What is the x-coordinate of the vertical asymptote of $f(x) = \log_3(x)$ ?

What is the amplitude of $y = -4\sin(x)$ ?

$-4$

$4$

$1$

$2\pi$

What is the period of $y = \sin(3x)$ ?

$3$

$6\pi$

$\dfrac{2\pi}{3}$

$2\pi$