SAT Mathematics Practice Test 5

Question : 14 of 58

Marks: +1, -0

$f(x)=2^x+1$
The function

f

is defined by the equation above.Which of the following is the graph of

y=−f(x )

in the

xy-

plane?

Validate

Solution:

The graph of

y=−f(x)

is the graph of the equation

y=−(2x+1),

y=−2x− 1.

This should be the graph of a decreasing exponential function. The y-intercept of the graph can be found by substituting the value x = 0 into the equation, as follows:

y=−20−1=−1-1=−2.

Therefore, the graph should pass through the point

(0, −2)

. Choice C is the only function that passes through this point.
Choices A and B are incorrect because the graphed functions are increasing instead of decreasing. Choice D is incorrect because the function passes through the point

(0,−1)

insteadof

(0, −2)

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