Logarithmic Functions Quiz

Graph the function y = log(x). Identify the y-intercept and x-intercept.

• The y-intercept is (0, 0) and the x-intercept is (1, 1).

• The y-intercept is (0, 1) and the x-intercept is (1, 0).

• The y-intercept is (1, 1) and the x-intercept is (0, 0).

• The y-intercept is (1, 0) and the x-intercept is (0, 1).

Compare the graphs of y = log(x) and y = log(x + 2). How are they different?

• The graph of y = log(x + 2) is steeper than the graph of y = log(x).

• The graphs are the same, but y = log(x + 2) is shifted 2 units to the right compared to y = log(x).

• The graphs are the same, but y = log(x + 2) is shifted 2 units to the left compared to y = log(x).

• The graph of y = log(x + 2) has a horizontal asymptote at x = 2.

Graph the function y = -log(x). Identify the y-intercept and x-intercept.

• Y-intercept: (0, 1), X-intercept: (1, 0)

• Y-intercept: (1, 0), X-intercept: (0, 0)

• Y-intercept: (0, 0), X-intercept: None

• Y-intercept: (0, 0), X-intercept: (0, 1)

Compare the graphs of y = -log(x) and y = log(-x). How are they different?

• The graphs are reflections of each other across the y-axis.

• The graphs intersect at the origin.

• The graphs are parallel to each other.

• The graphs have the same concavity.

Graph the function y = log(x) + 3. Identify the y-intercept and x-intercept.

• No y-intercept, x-intercept at (0.001, 0)

• y-intercept at (0, 3), x-intercept at (0.001, 0)

• No x-intercept, y-intercept at (0, 3)

• y-intercept at (0, 0), x-intercept at (0.001, 3)

Compare the graphs of y = log(x) and y = log(x) + 3. How are they different?

• The graphs are the same, but y = log(x) + 3 is shifted 3 units down compared to y = log(x).

• The graphs are the same, but y = log(x) + 3 is shifted 3 units up compared to y = log(x).

• The graphs are mirror images of each other.

• The graphs are different shapes and sizes.

Graph the function y = log(2x). Identify the y-intercept and x-intercept.

• The y-intercept is (0, 1) and the x-intercept is (0, 2)

• The y-intercept is (1, 0) and the x-intercept is (2, 0)

• The y-intercept is (0, undefined) and the x-intercept is (1/2, 0)

• The y-intercept is (1, 1) and the x-intercept is (1, 1)

Compare the graphs of y = log(x) and y = log(2x). How are they different?

• The graph of y = log(2x) is a horizontal translation of the graph of y = log(x) by 2 units.

• The graph of y = log(2x) is a stretched version of the graph of y = log(x) shifted to the right by a factor of 2.

• The graph of y = log(2x) is a compressed version of the graph of y = log(x) shifted to the left by a factor of 2.

• The graph of y = log(2x) is a reflection of the graph of y = log(x) over the x-axis.

Graph the function y = log(x) - 2. Identify the y-intercept and x-intercept.

• The y-intercept is at (0, 2) and the x-intercept is at (1, 0)

• The y-intercept is at (0, -1) and the x-intercept is at (1, 0)

• The y-intercept is at (0, 0) and the x-intercept is at (0, -2)

• The y-intercept is at (0, -2) and the x-intercept does not exist.

Compare the graphs of y = log(x) and y = log(x) - 2. How are they different?

• The graph of y = log(x) - 2 is a reflection of y = log(x) over the x-axis.

• The graph of y = log(x) - 2 is a horizontal compression of y = log(x).

• The graph of y = log(x) - 2 is a vertical shift of y = log(x) by 2 units to the right.

• The graph of y = log(x) - 2 is the same as y = log(x) but shifted 2 units downwards.