Grade 11 · Math · Algebra 2

11th grade Graph logarithmic functions worksheet

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Graph logarithmic functions

Grade 11 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

1.
Ren plots points from a log table and joins them with a curve. Which equation matches the graph?
- y = log₃ (x + 2)
- y = log₃ x
- y = 3^(x + 2)
- y = log₃ (x − 2)
2.
Tala plots points from a log table and joins them with a curve. Which equation matches the graph?
- y = log₂ x + 1
- y = 2^x − 1
- y = log₂ x − 1
- y = log₂ x
3.
Bo swaps the x and y columns of the table for y = 2^(x − 4). Which equation gives the new table, the inverse?
- y = log₂ x + 4
- y = log₂ (x − 4)
- y = log₂ x − 4
- y = 1/(2^(x − 4))
Esme graphs y = log₄ x + 3/2. At what value of x does the graph cross the x-axis?
Jun graphs y = log₉ x − 1/2. At what value of x does the graph cross the x-axis?
Kira graphs y = log₂ (x + 7). At what value of x does the graph cross the x-axis?
Luz graphs y = log₅ (x − 14). At what value of x does the graph cross the x-axis?
Milo reads the graph of y = log₈ (x + 4). What is y when x = 12?
Pia reads the graph of y = log₂₇ x + 2. What is y when x = 9?
Ren reads the graph of y = log₁₆ (x − 4). What is y when x = 12?

Graphs of logarithmic functions. Every version has 10 questions, and the answer key prints on the second page.

I can graph y = log₂ x by swapping the x and y columns of the y = 2^x table.
I can name the vertical asymptote, the domain, the range and the x-intercept of a log graph, shifted or not.
I can read a point on a shifted log graph, match a log graph to its equation, and write the inverse of y = 2^x + 3.

Standard: F-IF.C.7e, F-BF.B.3

logarithmic function: y = log_b x: the row of the × b table that gives x.

vertical asymptote: A wall the graph gets close to but never touches.

domain: All the x-values the graph uses.

range: All the y-values the graph reaches.

x-intercept: The point where the graph crosses the x-axis, where y = 0.

inverse: The function that undoes another; its graph is the mirror over y = x.

shift: Moving the whole graph left, right, up or down.

Said the log graph levels off at y = 0, which is true of y = 2^x, not of the log graph. Sketch both on one grid together and find each wall.

Moved the graph the wrong way: log₂ (x − 3) moves right 3, not left.

Used the plain log graph and left out the shift. Ask your child to point to the shift in the equation first.

Ask: what x makes x − 3 equal 0?

What is the most common mistake with graph logarithmic functions?

Said the log graph levels off at y = 0, which is true of y = 2^x, not of the log graph. Sketch both on one grid together and find each wall.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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