Exercises for Question Type 2: Drawing logarithmic functions as inverses of the exponential functions - IB

Report an issue

Exercises for Question Type 2: Drawing logarithmic functions as inverses of the exponential functions - IB

Written by IB Experts

Question 1

Sketch y = 5^{2 x} and its inverse y = \frac{1}{2} lo g_{5} (x) . Label asymptotes, the line y = x, the points (0, 1) and (\frac{1}{2}, 5), and their images.

[5]

Question 2

Sketch y = 3^{- x} and its inverse y = - lo g_{3} (x) . Label asymptotes, line y = x, and images of (0, 1) and (1, \frac{1}{3}) .

[4]

Question 3

Sketch y = e^{x - 1} and its inverse y = ln (x) + 1 . Label the asymptotes, the line y = x, and the images of (1, 1) and (2, e) .

[5]

Question 4

Sketch y = 5^{x + 2} - 1 and its inverse. State the equation of the inverse before sketching.

[5]

Question 5

Sketch the graphs of y = e^{x} and its inverse y = ln (x) on the same axes. Label the asymptotes, the line y = x, and the points corresponding to (0, 1) and (1, e) with their reflections.

[5]

Question 6

Sketch the graph of y = lo g_{1/2} (x) and its inverse y = (1/2)^{x} . Label the asymptotes, the line y = x, and the points (1, 0) and (2, - 1) along with their reflections.

[5]

Question 7

Consider the function f (x) = \frac{1}{3} e^{x - 1} . Find the equation of the inverse function, f^{- 1} (x) . Hence, sketch the graphs of f and f^{- 1} on the same set of axes, indicating the relationship between them.

[7]

Question 8

Sketch y = e^{x - 1} and its inverse y = ln (x) + 1 . Label the asymptotes, the line y = x, and the images of (1, 1) and (2, e) .

[5]

Question 9

Sketch y = 5^{x} and its inverse y = lo g_{5} (x), labelling the asymptotes, the line y = x, and the key points (0, 1) and (1, 5) with their reflections.

[4]

Question 10

Sketch y = lo g_{3} (x - 4) + 2 and its inverse. Determine the inverse explicitly before sketching.

[6]

Question 11

On one set of axes, sketch y = 2^{x} + 3 and its inverse y = lo g_{2} (x - 3) . Label the asymptotes, the line y = x, and key points.

[4]

Question 12

Find the expression for the inverse function of y = \frac{l n ( x )}{2 l n ( 5 )} . Sketch both functions on the same set of axes. Label asymptotes, the line y = x, and the points (1, 0) and (5, \frac{1}{2}) along with their reflections.

[5]