Questions: Without graphing, describe the shape of the graph of the function. Find the second coordinates of the points with first coordinates 0 and 1. f(x)=0.9^x The graph Find the second coordinates of the given first coordinates. x f(x)=0.9^x 0 f(0)= 1 f(1)= (Round to one decimal place as needed.)

Without graphing, describe the shape of the graph of the function. Find the second coordinates of the points with first coordinates 0 and 1.

f(x)=0.9^x

The graph

Find the second coordinates of the given first coordinates.

x f(x)=0.9^x
0 f(0)=
1 f(1)=

(Round to one decimal place as needed.)

Transcript text: point(s) possible Without graphing, describe the shape of the graph of the function. Find the second coordinates of the points with first coordinates 0 and 1. \[ f(x)=0.9^{x} \] The graph $\square$ Find the second coordinates of the given first coordinates. \[ \begin{array}{ll} x & f(x)=0.9^{x} \\ 0 & f(0)=\square \\ 1 & f(1)=\square \end{array} \] (Round to one decimal place as needed.)

Solution

Solution Steps

Step 1: Identifying the Shape of the Graph

The graph of the function grows exponentially because the coefficient of x in the exponent (1) is positive.

Step 2: Finding Specific Values

When $x = 0$, $f(0) = 0.9^{0*1} = 1$, since any non-zero number raised to the power of 0 is 1. When $x = 1$, $f(1) = 0.9^{1} = 0.9$, which is the value of the function at $x = 1$.