Exercises: Graphing Exponential, Logarithmic, and Trigonometric Functions

Show your work for each problem. Identify all key features as directed.

Grade 9·21 problems·~30 min·Common Core Math - HS Functions·standard·hsf-if-c-7e

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Warm-Up: Review What You Know

These problems review skills you have already learned.

Which of the following expressions is equivalent to $2^{-3}$ ?

$-8$

$\frac{1}{8}$

$\frac{1}{6}$

$-\frac{1}{8}$

The graph of $f(x) = 3^x$ is shifted down 5 units. What is the equation of the transformed function?

$f(x) = 3^{x-5}$

$f(x) = 3^x + 5$

$f(x) = 3^x - 5$

$f(x) = 3^{x+5}$

The parent function $y = \sin(x)$ has a maximum value of 1 and a minimum value of $-1$ .
What is the amplitude of the parent sine function?

$-1$

Apply the graphing procedures and identify key features.

For the exponential function $f(x) = 4 \cdot 2^x$ , what is the $y$ -intercept?

$(0, 2)$

$(0, 1)$

$(0, 8)$

$(0, 4)$

The function $h(x) = 5 \cdot \left(\frac{1}{3}\right)^x - 2$ has a horizontal asymptote.
What is the $y$ -value of the horizontal asymptote?

Which of the following correctly states the domain and range of $f(x) = \log_2(x)$ ?

Domain: all real numbers; Range: $y > 0$

Domain: $x > 0$ ; Range: all real numbers

Domain: $x > 0$ ; Range: $y > 0$

Domain: all real numbers; Range: all real numbers

$Graph of y = 3 sin(2x) + 1 showing amplitude of 3 from midline to peak, period of pi, and midline at y = 1$

For the function $y = 3\sin(2x) + 1$ , what is the amplitude?

$-3$

What is the period of the function $y = \cos\!\left(\frac{\pi}{3}x\right)$ ?

Express your answer as a number.

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