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Grade 11 · Math · Algebra 2

11th grade Graph logarithmic functions worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Graph logarithmic functions

Grade 11 Math Worksheet - Building Confidence

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

  1. Read this first

    Table for y = 2^x

    x = -1, y = 1/2; x = 0, y = 1; x = 1, y = 2; x = 2, y = 4; x = 3, y = 8.

  2. Milo swaps the x and y columns of the y = 2^x table to graph y = log₂ x. Which point on y = log₂ x comes from the row x = 3?

    • (3, 8)
    • (-3, 8)
    • (8, 3)
    • (3, -8)

  3. Table for y = 3^x

    x = -1, y = 1/3; x = 0, y = 1; x = 1, y = 3; x = 2, y = 9.

  4. Noah swaps the x and y columns of the y = 3^x table to graph y = log₃ x. Which point on y = log₃ x comes from the row x = 2?

    • (9, 2)
    • (2, -9)
    • (2, 9)
    • (-2, 9)

  5. Table for y = 5^x

    x = -1, y = 1/5; x = 0, y = 1; x = 1, y = 5; x = 2, y = 25.

  6. Pia swaps the x and y columns of the y = 5^x table to graph y = log₅ x. Which point on y = log₅ x comes from the row x = -1?

    • (-1, -1/5)
    • (-1, 1/5)
    • (1, 1/5)
    • (1/5, -1)

  7. Table for y = log₄ x

    x = 1/16, y = -2; x = 1/4, y = -1; x = 1, y = 0; x = 4, y = 1; x = 16, y = 2.

  8. Ren sketches y = log₄ x from its table of points. What is the vertical asymptote of y = log₄ x?

    • y = 0
    • x = 0
    • x = 1
    • y = 1

  9. Zee graphs y = ln x with a graphing app. What is the vertical asymptote of y = ln x?

    • x = 0
    • y = 0
    • x = 1
    • y = 1

  10. Table for y = log₃ x

    x = 1, y = 0; x = 3, y = 1; x = 9, y = 2; x = ?, y = 4.

  11. Bo fills in the table for y = log₃ x by swapping the columns of the y = 3^x table. What x goes in the row where y = 4?

  12. Table for y = log₅ x

    x = 1, y = 0; x = 5, y = 1; x = 25, y = 2; x = ?, y = 3.

  13. Esme fills in the table for y = log₅ x by swapping the columns of the y = 5^x table. What x goes in the row where y = 3?

  14. Jun studies the graph of y = log₂ x. What is the domain of y = log₂ x?

    • x > 1
    • x ≥ 0
    • all real numbers
    • x > 0

  15. Kira studies the graph of y = log₃ x. What is the range of y = log₃ x?

    • y ≥ 0
    • all real numbers
    • y > 1
    • y > 0

  16. Luz studies the graph of y = log x. What is the domain of y = log x?

    • x > 0
    • x ≥ 0
    • x > 1
    • all real numbers
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11th grade Graph logarithmic functions worksheet – printable
Print: 123456

About this worksheet

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

What your child will learn

  • 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

Words to know

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.

Common mistakes

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.

What to say

Ask: what x makes x − 3 equal 0?

Questions parents ask

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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