Question

Explain how to graph this exponential function.

Be sure to:


describe the domain and range

describe x- and y- intercepts

create a table of vaules and points

Graph x


`f(x)=0.4^(x) -1`

Answer 1

The domain is -∞ < x < ∞

The range is y > -1

The x-intercept is 0

The y-intercept is 0

Explanation:

∵ f(x) = 0.4^x - 1

∴ The domain is all real numbers -∞ < x < ∞

∴ The range of it is y > -1

Note: If the range of f(x) = b^x , where b > 0 and b ≠ 1 is y > 0 ,

If f(x) is shifted down 1 unit (f(x) - 1) , then the range will be y > -1

∵ f(x) = 0 ⇒ 0.4^x - 1 = 0

∴ 0.4^x = 1 ⇒ ∴ x = 0

∴ The x-intercept is 0

∵ f(0) = 0.4^0 - 1 = 1 - 1 = 0

∴ The y-intercept is 0

∴ The graph of f(x) = 0.4^x - 1 passing through the origin point

Table:

x ⇒ f(x)

-2 ⇒ 5.25

-1 ⇒ 1.5

0 ⇒ 0

1 ⇒ -0.6

2 ⇒ -0.84