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)

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

(−2,80), (−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)
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,−2.5), (1,1.25), (0,0) and (1,1.2)

GPT-4o mini · Answer

To find the y-values of the function $ y = 5(1/4)^x $ for the given x-values, we will substitute each x-value into the equation: 1. For $ x = -2 $: $$ y = 5\left(\frac{1}{4}\right)^{-2} = 5 \times 4^2 = 5 \times 16 = 80 $$ 2. For $ x = -1 $: $$ y = 5\left(\frac{1}{4}\right)^{-1} = 5 \times 4^1 = 5 \times 4 = 20 $$ 3. For $ x = 0 $: $$ y = 5\left(\frac{1}{4}\right)^{0} = 5 \times 1 = 5 $$ 4. For $ x = 1 $: $$ y = 5\left(\frac{1}{4}\right)^{1} = 5 \times \frac{1}{4} = 5 \times 0.25 = 1.25 $$ Putting the ordered pairs together, we have: - For $ x = -2 $: $ (−2, 80) $ - For $ x = -1 $: $ (−1, 20) $ - For $ x = 0 $: $ (0, 5) $ - For $ x = 1 $: $ (1, 1.25) $ Thus, the correct set of ordered pairs is: **(−2, 80), (−1, 20), (0, 5), and (1, 1.25)**.