A curve with arrows at both the ends facing upward is plotted on a coordinate plane with x and y axes ranging from negative 10 to 10 in unit increments.
Determine the range of the exponential function f(x)=3(1/2)^x−6
.
(1 point)
Responses
y≥−6
y greater-than-or-equal-to negative 6
y>−6
y greater than negative 6
y>6
y greater than 6
y<−6
Use the image to answer the question.
A descending curve is graphed in quadrant 1 of a coordinate plane. The points left parenthesis 1 comma 14 right parenthesis and left parenthesis 2 comma 4 right parenthesis are plotted on the curve. The curve descends to but does not cross the x-axis.
An exponential function is described by the equation h(x)=49(2/7)x
. Which inequality describes the range of this function?
(1 point)
Responses
0<y<16
0 less than y less than 16
y>0
y greater than 0
y≥0
y greater-than-or-equal-to 0
−∞<y<∞
Graph the exponential function y=0.5(6)x
. Identify the y-intercept.(1 point)
Responses
−4
negative 4
0.5
0.5
1
1
0
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,−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)
Use the image to answer the question.
A curve and two labeled points on the curve are plotted in quadrant 1 of a coordinate plane.
Given the graph of the exponential equation, write the correct exponential equation for the graph.
(1 point)
Responses
y=3(3/2)x
y equals 3 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline
y=3(2/3)x
y equals 3 left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript x baseline
y=2(3/2)x
y equals 2 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline
y=3/2(3)x
y equals Start Fraction 3 over 2 End Fraction left parenthesis 3 right parenthesis superscript x baseline
1 answer
Let's break down each question you provided and determine the correct responses.
Range of the function \(f(x) = 3(1/2)^x - 6\):
The base \(1/2\) is less than 1, thus the function decreases as \(x\) increases. As \(x\) approaches negative infinity, \(f(x)\) approaches positive infinity, and as \(x\) approaches positive infinity, \(f(x)\) approaches \(-6\). Thus, the range is:
Response: \(y \ge -6\)
Range of the function \(h(x) = 49(2/7)^x\):
Again, since \(2/7 < 1\), this function also decreases as \(x\) increases. As \(x\) approaches negative infinity, \(h(x)\) approaches positive infinity, and as \(x\) approaches positive infinity, \(h(x)\) approaches 0, but never actually reaches it. Thus, the range is:
Response: \(y > 0\)
Y-intercept of the function \(y = 0.5(6)^x\):
The y-intercept occurs when \(x = 0\). Substituting \(x = 0\):
\[
y = 0.5(6)^0 = 0.5(1) = 0.5
\]
Response: \(0.5\)
Ordered pairs for the function \(y = 5(1/4)^x\) with x-values -2, -1, 0, and 1:
Let's calculate the corresponding \(y\)-values:
For \(x = -2\):
\[
y = 5(1/4)^{-2} = 5(4) = 20
\]
For \(x = -1\):
\[
y = 5(1/4)^{-1} = 5(4) = 20
\]
For \(x = 0\):
\[
y = 5(1/4)^{0} = 5(1) = 5
\]
For \(x = 1\):
\[
y = 5(1/4)^{1} = 5(0.25) = 1.25
\]
The ordered pairs are:
Response: \((−2,80), (−1,20), (0,5), (1,1.25)\)
Write the correct exponential equation based on the description:
If the curve starts and grows according to the points and characteristics described, you would choose the parameterization consistent with the shape and growth described.
Since I don't have details about the graph and points, I cannot confirm the exact equation based on visual information. Generally, check the base's value to see if it's greater or less than 1 to determine if it's increasing or decreasing.
If the function is increasing, it should be an equation with a base greater than 1, and one with a base less than 1 if it's decreasing.
Given this analysis, you should revise selections based on the specific graph characteristics you see, especially for the last question.
