Question

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

Answer 1

To graph the function \( y = 15(2^x) \) and find the y-intercept, we need to evaluate the function when \( x = 0 \).

1. **Finding the y-intercept:**
\[
y = 15(2^0)
\]
Since \( 2^0 = 1 \),
\[
y = 15 \times 1 = 15
\]

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

2. **Graphing the function:**
To graph the function \( y = 15(2^x) \), we can calculate a few additional points by selecting values for \( x \):

- For \( x = -1 \):
\[
y = 15(2^{-1}) = 15 \times \frac{1}{2} = 7.5 \quad \text{(Point: (-1, 7.5))}
\]
- For \( x = 1 \):
\[
y = 15(2^1) = 15 \times 2 = 30 \quad \text{(Point: (1, 30))}
\]
- For \( x = 2 \):
\[
y = 15(2^2) = 15 \times 4 = 60 \quad \text{(Point: (2, 60))}
\]

Now, you can plot these points on the graph:

- The point \( (0, 15) \) is the y-intercept.
- The point \( (-1, 7.5) \) is close to the y-axis.
- The points \( (1, 30) \) and \( (2, 60) \) show the rapid increase of the function as \( x \) increases.

The graph will show exponential growth as \( x \) increases. The y-intercept is \( 15 \) at \( (0, 15) \).