Exponents and Logarithms · Ages 16–17
Graphing Exponential and Logarithmic Functions
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This worksheet is for 11th-grade math students. Identify the intercepts, asymptotes, and general shape for each curve before sketching.
State the y-intercept and horizontal asymptote for y = 3^x.
Does the graph of y = (1/3)^x rise or fall from left to right, and what is its horizontal asymptote?
Find the x-intercept, vertical asymptote, and domain for y = log3(x).
What is the relationship between the graph of y = 4^x and y = log4(x)?
Determine the vertical asymptote and domain for the transformed function y = log2(x - 3).
Determine the horizontal asymptote and y-intercept for y = 2^x - 4.
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State the y-intercept and horizontal asymptote for y = 3^x.
y-intercept is (0, 1); horizontal asymptote is y = 0.
Does the graph of y = (1/3)^x rise or fall from left to right, and what is its horizontal asymptote?
It falls from left to right (decay); horizontal asymptote is y = 0.
Find the x-intercept, vertical asymptote, and domain for y = log3(x).
x-intercept is (1, 0); vertical asymptote is x = 0; domain is x > 0.
What is the relationship between the graph of y = 4^x and y = log4(x)?
They are reflections of each other across the diagonal line y = x.
Determine the vertical asymptote and domain for the transformed function y = log2(x - 3).
Vertical asymptote is x = 3; domain is x > 3.
Determine the horizontal asymptote and y-intercept for y = 2^x - 4.
Horizontal asymptote is y = -4; y-intercept is (0, -3).