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 (−2,0.45) , (−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,−2.5) , (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)
Answers
Answered by
GPT-4o mini
To find the ordered pairs for the function \( y = 5\left(\frac{1}{4}\right)^x \) at the specified x-values of -2, -1, 0, and 1, we need to compute the y-values for these x-values:
1. **For \( x = -2 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{-2} = 5\left(4\right) = 20
\]
Thus, the point is \( (-2, 20) \).
2. **For \( x = -1 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{-1} = 5\left(4\right) = 20
\]
Thus, the point is \( (-1, 20) \).
3. **For \( x = 0 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{0} = 5\left(1\right) = 5
\]
Thus, the point is \( (0, 5) \).
4. **For \( x = 1 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{1} = 5\left(\frac{1}{4}\right) = \frac{5}{4} = 1.25
\]
Thus, the point is \( (1, 1.25) \).
Putting these together, the ordered pairs are:
- \( (-2, 20) \)
- \( (-1, 20) \)
- \( (0, 5) \)
- \( (1, 1.25) \)
From the given options, it seems like there is just one set of answers you mentioned that matches any values from our calculations:
- \( (-2, 80) \), \( (-1, 20) \), \( (0, 5) \), and \( (1, 1.25) \)
However, the correct results should be:
- \( (-2, 20) \), \( (-1, 20) \), \( (0, 5) \), and \( (1, 1.25) \).
So, out of the options you listed, the closest is:
- \( (-1, 20) \), \( (0, 5) \), and \( (1, 1.25) \) in the context of y-values computed.
If you have any confusion or need additional calculations, feel free to ask!
1. **For \( x = -2 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{-2} = 5\left(4\right) = 20
\]
Thus, the point is \( (-2, 20) \).
2. **For \( x = -1 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{-1} = 5\left(4\right) = 20
\]
Thus, the point is \( (-1, 20) \).
3. **For \( x = 0 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{0} = 5\left(1\right) = 5
\]
Thus, the point is \( (0, 5) \).
4. **For \( x = 1 \)**:
\[
y = 5\left(\frac{1}{4}\right)^{1} = 5\left(\frac{1}{4}\right) = \frac{5}{4} = 1.25
\]
Thus, the point is \( (1, 1.25) \).
Putting these together, the ordered pairs are:
- \( (-2, 20) \)
- \( (-1, 20) \)
- \( (0, 5) \)
- \( (1, 1.25) \)
From the given options, it seems like there is just one set of answers you mentioned that matches any values from our calculations:
- \( (-2, 80) \), \( (-1, 20) \), \( (0, 5) \), and \( (1, 1.25) \)
However, the correct results should be:
- \( (-2, 20) \), \( (-1, 20) \), \( (0, 5) \), and \( (1, 1.25) \).
So, out of the options you listed, the closest is:
- \( (-1, 20) \), \( (0, 5) \), and \( (1, 1.25) \) in the context of y-values computed.
If you have any confusion or need additional calculations, feel free to ask!
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