Graph f(x)=(0.4)^x

Identify the type of function. This is an exponential function of the form ƒ(x)=bx where the base b=0.4 Since 0<0.4<1 the function represents exponential decay.

Determine the y-intercept. By substituting x=0 we find ƒ(0)=(0.4)0=1 The graph passes through (0,1)

Calculate additional points to define the shape.
For x=1 ƒ(1)=0.4
For x=2 ƒ(2)=0.16
For x=−1 ƒ*(−1)=(0.4)(−1)=1/0.4=2.5
For x=−2 ƒ*(−2)=(0.4)(−2)=1/0.16=6.25

Identify the horizontal asymptote. As x increases toward infinity, (0.4)x approaches 0 Therefore, the horizontal asymptote is the x-axis, y=0

Sketch the curve. Draw a smooth curve that decreases from left to right, passing through the calculated points and approaching the x-axis as x becomes large.

Graph f(x)=(0.4)^x

Problem

Solution

Final Answer