Let , and define two functions and . Which of the following best describes the graph…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f(t)=t^{2}+1

, and define two functions

G(x)=1+\displaystyle\int_{0}^{x} f(t)\,dt

and

H(x)=5+\displaystyle\int_{0}^{x} f(t)\,dt

. Which of the following best describes the graph of

H

relative to the graph of

G

? (a)

H

is obtained by translating the graph of

G

upward by

4x

units. (b)

H

is obtained by translating the graph of

G

to the right by

4

units. (c)

H

is obtained by translating the graph of

G

upward by

4

units. (d)

H

is obtained by translating the graph of

G

downward by

4

units.