Question

Given the function f(x) = −3^2 + 4x + 6, find f(2) and f(3). Choose the statement that is true concerning these two values.

A.) The value of f(2) is the same as the value of f(3).
B.) The value of f(2) cannot be compared to the value of f(3).
C.) The value of f(2) is smaller than the value of f(3).
D.) The value of f(2) is larger than the value of f(3).

Answer 1

The answer is statement D.

Explanation:

In order to determine the true statement, we have to solve every statement.

In any function, we replace any allowed "x" value and the function gives us a value. This process is called "evaluating function". If we want to compare different values of the function for different "x" values, we just have to evaluate them first and then compare.

So, for x=2 and x=3

f(2)=-3*(2)^2+4*2+6=-12+8+6=2

f(3)=-3*(3)^2+4*3+6=-27+12+6=-9

f(2)>f(3)

According to the possible options, the true statement is D.

Answer 2

D (assuming f(x)=-3x^2+4x+6)

Explanation:

Let's find f(2) and f(3).

I'm going to make the assumption you meant f(x)=-3x^2+4x+6 (please correct if this is not the function you had).

f(2) means replace x with 2.

f(2)=-3(2)^2+4(2)+6

Use pemdas to simplify: -3(4)+4(2)+6=-12+8+6=-4+6=2.

So f(2)=2

f(3) means replace x with 3.

f(3)=-3(3)^2+4(3)+6

Use pemdas to simplify: -3(9)+4(3)+6=-27+12+6=-15+6=-9

So f(3)=-9

-9 is smaller than 2 is the same as saying f(3) is smaller than f(2) or that f(2) is bigger than f(3).