Question

Graph the function y=15(2)^x
. What is the y-intercept?(1 point)

Answer 1

To graph the function \( y = 15(2)^x \), we can identify characteristics of the function including the y-intercept.

1. **Find the y-intercept**: The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the function:

\[
y = 15(2)^0 = 15(1) = 15
\]

Therefore, the y-intercept is \( (0, 15) \).

2. **Graph the function**: To sketch the graph of \( y = 15(2)^x \), we calculate a few values of \( y \) for various \( x \):
- For \( x = -2 \):
\[
y = 15(2)^{-2} = 15 \cdot \frac{1}{4} = 3.75
\]
- For \( x = -1 \):
\[
y = 15(2)^{-1} = 15 \cdot \frac{1}{2} = 7.5
\]
- For \( x = 0 \):
\[
y = 15(2)^0 = 15
\]
- For \( x = 1 \):
\[
y = 15(2)^1 = 30
\]
- For \( x = 2 \):
\[
y = 15(2)^2 = 60
\]

3. **Plot these points**: The points \( (-2, 3.75) \), \( (-1, 7.5) \), \( (0, 15) \), \( (1, 30) \), \( (2, 60) \) can be plotted on a graph.

4. **Shape of the graph**: Since \( y = 15(2)^x \) is an exponential function with a base greater than 1, the graph will rise sharply as \( x \) increases, and approach \( 0 \) as \( x \) decreases.

Thus, the y-intercept of the function \( y = 15(2)^x \) is:

\[
\text{Y-intercept: } (0, 15)
\]