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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,−2.5)
, (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

(−2,0.45)
, (−1,0.67)
, (0,1)
, and (1,1.50)
left parenthesis negative 2 comma 0.45 right parenthesis , left parenthesis negative 1 comma 0.67 right parenthesis , left parenthesis 0 comma 1 right parenthesis , and left parenthesis 1 comma 1.50 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,−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

1 answer

To find the y-values for the function \( y = 5(1/4)^x \) at the given x-values (-2, -1, 0, and 1), we can plug these values into the function:

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

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

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

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

Now, we can summarize the ordered pairs:

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

So the correct set of ordered pairs based on the given options is: \( (-2, 80) \), \( (-1, 20) \), \( (0, 5) \), and \( (1, 1.25) \).

The correct match is: (−2,80), (−1,20), (0,5), and (1,1.25).