1. Exploring Exponential Models - 7. Exponential and Logarithmic Functions

a Notice that the format of the given function resembles that of the vertex form of a quadratic function.

\underline{Vertex Form} y = a (x - h)^{2} + k

By rewriting our function a bit, we can confirm that it is given in this form indeed.

y = 3 (x + 1)^{2} ⇕ y = 3 (x - (- 1))^{2} + 0

Therefore, this is a quadratic function.

b Notice that the format of the given function resembles that of an exponential function.

\underline{Exponential Function} y = a (b)^{x}

By direct comparison, we can confirm that it is given in this form indeed.

y = 4 (3)^{x}

Therefore, this is an exponential function.

c Notice that the format of the given function resembles that of the slope-intercept form of a linear function.

\underline{Slope - Intercept Form} y = m x + b

By direct comparison, we can confirm that it is given in this form indeed.

y = 2 x + 5

Therefore, this is a linear function.

d Notice that the format of the given function resembles that of an exponential function.

\underline{Exponential Function} y = a (b)^{x}

By direct comparison, we can confirm that it is an exponential function indeed. The only difference is that it has been

translated

up

by

1

unit

y = 4 (3)^{x} + 1

Exercise 8 Page 439