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.(1 point)
Responses

(−2,80)
, (−1,20)
, (0,5)
, and (1,1.25)
left parenthesis negative 2 comma 80 right parenthesis , left parenthesis negative 1 comma 20 right parenthesis , left parenthesis 0 comma 5 right parenthesis , and left parenthesis 1 comma 1.25 right parenthesis

(−2,−2.5)
, (1,1.25)
, (0,0)
and (1,1.2)
left parenthesis negative 2 comma negative 2.5 right parenthesis , left parenthesis 1 comma 1.25 right parenthesis , left parenthesis 0 comma 0 right parenthesis and left parenthesis 1 comma 1.2 right parenthesis

(−2,−2.99)
, (−1,−1.49)
, (0,0)
, and (1,1.49)
left parenthesis negative 2 comma negative 2.99 right parenthesis , left parenthesis negative 1 comma negative 1.49 right parenthesis , left parenthesis 0 comma 0 right parenthesis , and left parenthesis 1 comma 1.49 right parenthesis

(−2,0.45)
, (−1,0.67)
, (0,1)
, and (1,1.50)

.

Answer 1

To find the ordered pairs for the function \( y = 5\left(\frac{1}{4}\right)^x \) for the given \( x \)-values of -2, -1, 0, and 1, we can plug in each value of \( x \) into the function:

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

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

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

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

Combining all the results, we have the ordered pairs:
\[
(-2, 80), (-1, 20), (0, 5), (1, 1.25)
\]

Thus, the correct response is:
**(−2,80), (−1,20), (0,5), and (1,1.25)**.