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,−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,−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

(−2,80)
, (−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

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

Answer 1

To find the ordered pairs for the function \( y = 5 \left( \frac{1}{4} \right)^x \), we can substitute the provided x-values (-2, -1, 0, and 1) into the function to calculate their corresponding y-values.

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

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

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

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

Now, we can summarize the calculated ordered pairs:
- \((-2, 20)\)
- \((-1, 5)\)
- \((0, 5)\)
- \((1, 1.25)\)

Among the provided options, the closest matching pairs are:

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

Thus, the correct response would be:
\[
(-2, 80), (-1, 20), (0, 5), (1, 1.25)
\]