The function 𝑓 is given by 𝑓(𝑥)=2(3𝑥). Which of the following statements describes characteristics of the graph of 𝑓 in the 𝑥𝑦-plane?ResponsesThe graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8𝑥.The graph of f is a vertical dilation of y equals 2 to the power of x , and f open parentheses x close parentheses is equivalent to 8 to the power of x .The graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8·2𝑥.The graph of f is a vertical dilation of y equals 2 to the power of x , and f open parentheses x close parentheses is equivalent to 8 times 2 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8𝑥.The graph of f is a horizontal dilation of y equals 2 to the power of x , and f open parentheses x close parentheses is equivalent to 8 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8·2𝑥.
Question
The function 𝑓 is given by 𝑓(𝑥)=2(3𝑥). Which of the following statements describes characteristics of the graph of 𝑓 in the 𝑥𝑦-plane?ResponsesThe graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8𝑥.The graph of f is a vertical dilation of y equals 2 to the power of x , and f open parentheses x close parentheses is equivalent to 8 to the power of x .The graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8·2𝑥.The graph of f is a vertical dilation of y equals 2 to the power of x , and f open parentheses x close parentheses is equivalent to 8 times 2 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8𝑥.The graph of f is a horizontal dilation of y equals 2 to the power of x , and f open parentheses x close parentheses is equivalent to 8 to the power of x .The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8·2𝑥.
Solution
The function 𝑓(𝑥)=2(3𝑥) is a linear function, where the slope is 2*3=6. This means that for every unit increase in x, the value of f(x) increases by 6 units.
Looking at the options:
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The graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8𝑥. - This is incorrect. The function is not equivalent to 8x, but 6x.
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The graph of f is a vertical dilation of y equals 2 to the power of x , and f(x) is equivalent to 8 to the power of x. - This is incorrect. The function is not equivalent to 8 to the power of x, but 6x.
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The graph of 𝑓 is a vertical dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8·2𝑥. - This is incorrect. The function is not equivalent to 8·2x, but 6x.
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The graph of f is a vertical dilation of y equals 2 to the power of x , and f(x) is equivalent to 8 times 2 to the power of x. - This is incorrect. The function is not equivalent to 8 times 2 to the power of x, but 6x.
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The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8𝑥. - This is incorrect. The function is not equivalent to 8x, but 6x.
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The graph of f is a horizontal dilation of y equals 2 to the power of x , and f(x) is equivalent to 8 to the power of x. - This is incorrect. The function is not equivalent to 8 to the power of x, but 6x.
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The graph of 𝑓 is a horizontal dilation of 𝑦=2𝑥, and 𝑓(𝑥) is equivalent to 8·2𝑥. - This is incorrect. The function is not equivalent to 8·2x, but 6x.
None of the given options correctly describe the characteristics of the graph of 𝑓 in the 𝑥𝑦-plane.
Similar Questions
In the 𝑥𝑦-plane, the function ℎ, given by ℎ𝑥=3𝑥+2, is a horizontal translation of the exponential function 𝑓, given by 𝑓𝑥=3𝑥. Which of the following is an equivalent form for ℎ𝑥 that expresses ℎ as a vertical dilation of 𝑓 ?Responsesℎ𝑥=3𝑥/2h open parentheses x close parentheses equals 3 to the power of open parentheses x divided by 2 close parentheses end exponentℎ𝑥=9·3𝑥h open parentheses x close parentheses equals 9 times 3 to the power of x ℎ𝑥=9·13𝑥h open parentheses x close parentheses equals 9 times open parentheses 1 third close parentheses to the power of x
Fill in the blanks to complete the statement:Compared to the graph of the parent function, 𝑓(𝑥)=|𝑥|𝑓(𝑥)=|𝑥|, the graph of 𝑔(𝑥)=𝑎|𝑥|𝑔(𝑥)=𝑎|𝑥|, where 𝑎>1𝑎>1, results in a vertical Answer 1 Question 11, making 𝑔(𝑥)𝑔(𝑥) Answer 2 Question 11 than the graph of 𝑓(𝑥)𝑓(𝑥).
Consider the functions below.𝑓(𝑥)=𝑥𝑔(𝑥)=15𝑥Which of the following statements describes the graph of function g? A. The graph of g is one-fifth as steep as the graph of f. B. The graph of g is one-fifth of a unit to the left of the graph of f. C. The graph of g is five times steeper than the graph of f. D. The graph of g is one-fifth of a unit to the right of the graph of f.
How does the graph of 𝑓(𝑥)=−32𝑥−4f(x)=−3 2x −4 differ from the graph of 𝑔(𝑥)=−32𝑥g(x)=−3 2x ?A.The graph of 𝑓(𝑥)f(x) is shifted four units to the right of the graph of 𝑔(𝑥)g(x).B.The graph of 𝑓(𝑥)f(x) is shifted four units down from the graph of 𝑔(𝑥)g(x).C.The graph of 𝑓(𝑥)f(x) is shifted four units up from the graph of 𝑔(𝑥)g(x).D.The graph of 𝑓(𝑥)f(x) is shifted four units to the left of the graph of 𝑔(𝑥)g(x).SUBMITarrow_backPREVIOUS
Which of the following correctly describes the graph of 𝑓(𝑥)=−4𝑥2+16𝑥−2 ?Group of answer choicesThe graph is an exponential function with a y-intercept at (2,14) and a horizontal asymptote at 𝑦=−2.The graph is a parabola with a vertex at (16,2), a y-intercept at (0,2), and the parabola opens down.The graph is a parabola with a vertex at (2,14), a y-intercept at (0,−2), and the parabola opens down.The graph is an exponential function with a y-intercept at (0,−2) and a horizontal asymptote at 𝑦=2.The graph is a parabola with a vertex at (2,14), a y-intercept at (0,2), and the parabola opens up.
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