Grade 11 · Math · Algebra 2

11th grade Graph logarithmic functions worksheet

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Graph logarithmic functions

Grade 11 Math Worksheet

NameDate

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

1.
Milo moves the graph of y = log₂ x to get y = log₂ (x − 7). What is the vertical asymptote of y = log₂ (x − 7)?
- x = 7
- x = -7
- x = 0
- y = 0
2.
Pia moves the graph of y = log₃ x to get y = log₃ (x − 1). What is the vertical asymptote of y = log₃ (x − 1)?
- x = 0
- y = 0
- x = -1
- x = 1
3.
Ren moves the graph of y = log₂ x to get y = log₂ (x + 2). What is the domain of y = log₂ (x + 2)?
- x ≥ -2
- x > 0
- x > 2
- x > -2
4.
Tala moves the graph of y = log₄ x to get y = log₄ (x − 5). What is the domain of y = log₄ (x − 5)?
- x > 5
- x > 0
- x ≥ 5
- x > -5
Bo graphs y = log₄ (x + 2). At what value of x does the graph cross the x-axis?
Esme graphs y = log₉ x − 3/2. At what value of x does the graph cross the x-axis?
Jun graphs y = log₂ x + 3. At what value of x does the graph cross the x-axis?
Kira reads the graph of y = log₂ (x − 3). What is y when x = 7?
Milo reads the graph of y = log₂ x + 5. What is y when x = 16?
Noah reads the graph of y = log₃ x − 4. What is y when x = 27?

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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