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The x-axis ranges from negative 1.6 to 1.6 in increments of 0.2 and the y-axis ranges from negative 4 to 26 in increments of 2. The curved line labeled f left parenthesis x right parenthesis equals 6 times 1.5
superscript x passes through left parenthesis negative 1.6 comma 3 right parenthesis, left parenthesis negative 1 comma 4 right parenthesis, left parenthesis 0 comma 6 right parenthesis, left parenthesis 0.6
comma 7.5 right parenthesis, left parenthesis 1 comma 9 right parenthesis, and left parenthesis 1.7 comma 12 right parenthesis. The straight line labeled g left parenthesis x right parenthesis equals 5 times x plus
10 passes through left parenthesis negative 1.6 comma 2 right parenthesis, left parenthesis 0 comma 10 right parenthesis, and left parenthesis 1.6 comma 18 right parenthesis. Both the curve and the straight line
have arrows at both ends. The line and the curve intersect at left parenthesis negative 1.3 comma 3.7 right parenthesis. All coordinate values are approximate, and the coordinates are unlabeled.

Marshall is comparing the growth rates of f(x) = 6 - 1.5 and g (x) = 5x + 10 using this graph. Based on the graph, he concludes that the growth rate of g (x) = 5x + 10 is always greater than the growth rate
of f(x)=6 .1.5. Where is his mistake?
(1 point)

O Marshall has it backward. The growth rate of f (x) = 6 . 1.52 is always greater than the growth rate of g (x) = 5x + 10.

Marshall is only considering a small portion of the domains of the functions. If he went farther to the left on the graph, he would observe that the growth rate of f (x) = 6 . 1.5 eventually surpasses the growth rate of
g() = 5x + 10 for negative values of x.

O The growth rate of g (x) = 5x + 10 is only greater than the growth rate of f (x) = 6 . 1.5 when a is greater than approximately -1.3.

Marshall is only considering a small portion of the domains of the functions. If he went farther to the right on the graph, he would observe that the growth rate of f (z) = 6 . 1.5 eventually surpasses the growth rate of
g(z) = 5x + 10 for large values of x.

All Answers 1

Answered by GPT-5 mini AI
Choose: "Marshall is only considering a small portion of the domains of the functions. If he went farther to the right on the graph, he would observe that the growth rate of f(x)=6·1.5^x eventually surpasses the growth rate of g(x)=5x+10 for large values of x."

Why: g has constant slope 5, but f's instantaneous growth f'(x)=6·ln(1.5)·1.5^x increases with x and exceeds 5 for x ≳ 1.78. Marshall confused the functions' values (or a small part of the graph) with their growth rates.