Question

Graph the function y=5(14)x
𝑦
=
5
(
1
4
)
𝑥
. Complete the ordered pairs for the x-values of −2
−
2
, −1
−
1
, 0, and 1 by finding the y-values.(1 point)
Responses

(−2,0.45)
(
−
2
,
0.45
)
, (−1,0.67)
(
−
1

Answer 1

To complete the ordered pairs, we need to compute the value of \( y \) for each given \( x \) in the function \( y = 5(14)^x \).

1. **For \( x = -2 \)**:
\[
y = 5(14)^{-2} = 5 \cdot \frac{1}{14^2} = 5 \cdot \frac{1}{196} = \frac{5}{196} \approx 0.0255
\]
\[
\text{Ordered Pair: } (-2, 0.0255)
\]

2. **For \( x = -1 \)**:
\[
y = 5(14)^{-1} = 5 \cdot \frac{1}{14} \approx 5 \cdot 0.07143 \approx 0.3571
\]
\[
\text{Ordered Pair: } (-1, 0.3571)
\]

3. **For \( x = 0 \)**:
\[
y = 5(14)^{0} = 5 \cdot 1 = 5
\]
\[
\text{Ordered Pair: } (0, 5)
\]

4. **For \( x = 1 \)**:
\[
y = 5(14)^{1} = 5 \cdot 14 = 70
\]
\[
\text{Ordered Pair: } (1, 70)
\]

Now we can summarize the ordered pairs:

- \( (-2, 0.0255) \)
- \( (-1, 0.3571) \)
- \( (0, 5) \)
- \( (1, 70) \)

Therefore, the complete set of ordered pairs is:

\[
(-2, 0.0255), (-1, 0.3571), (0, 5), (1, 70)
\]