Question

Graph the function y=5(1/4)^x
. Complete the ordered pairs for the x-values of −2
, −1
, 0, and 1 by finding the y-values.

Answer 1

To graph the function \( y = 5 \left( \frac{1}{4} \right)^x \) and find the ordered pairs for the specified x-values, we will calculate the corresponding y-values.

Let's calculate the y-values for the given x-values:

1. For \( x = -2 \):
\[
y = 5 \left( \frac{1}{4} \right)^{-2} = 5 \left( \frac{4}{1} \right)^{2} = 5 \times 16 = 80
\]
So, the ordered pair is \( (-2, 80) \).

2. For \( x = -1 \):
\[
y = 5 \left( \frac{1}{4} \right)^{-1} = 5 \left( \frac{4}{1} \right)^{1} = 5 \times 4 = 20
\]
So, the ordered pair is \( (-1, 20) \).

3. For \( x = 0 \):
\[
y = 5 \left( \frac{1}{4} \right)^{0} = 5 \times 1 = 5
\]
So, the ordered pair is \( (0, 5) \).

4. For \( x = 1 \):
\[
y = 5 \left( \frac{1}{4} \right)^{1} = 5 \times \frac{1}{4} = \frac{5}{4} = 1.25
\]
So, the ordered pair is \( (1, 1.25) \).

Now, we have the following ordered pairs:

- \( (-2, 80) \)
- \( (-1, 20) \)
- \( (0, 5) \)
- \( (1, 1.25) \)

You can plot these points on a coordinate graph to visualize the function \( y = 5 \left( \frac{1}{4} \right)^x \). The graph will show a decreasing exponential function.