Chapter 8

8.1 Exploring the Logarithmic
Function
YOU WILL NEED
• graph paper
GOAL
Investigate the inverse of the exponential function.
EXPLORE the Math
6
4
y
y = x
6
4
y
y = x 2
2
y = 2x + 1
–6 –4 –2
0
–2
–4
2 4 6 x
y = x – 1
2
2
–6 –4 –2
0
–2
–4
2 4 6 x
y = ± √x
–6
–6
The inverse of a linear function,
such as f (x) 5 2x 1 1, is linear.
The inverse of a quadratic
function, such as g(x) 5 x 2 , has a
shape that is congruent to the
shape of the original function.
?
What does the graph of the inverse of an exponential function
like y 5 2 x look like, and what are its characteristics?
A. Consider the function h(x) 5 2 x . Create a table of values, using
integer values for the domain 23 # x # 4.
B. On graph paper, graph the exponential function in part A. State the
domain and range of this function.
C. Interchange x and y in the equation for h to obtain the equation of the
inverse relation. Create a table of values for this inverse relation. How
does each y-value of this relation relate to the base, 2, and its
corresponding x-value?
448 8.1 Exploring the Logarithmic Function
NEL