Question 734·Easy·Math

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The function $g$ is defined by

g(x) = (x + 0.2x)(60 - 2x)

What is the value of $g(10)$ ?

A function evaluation gives you an input and asks for the output of a rule. Replace every copy of the variable with that input, keeping the signs and parentheses in each factor. Define the rule in Desmos and evaluate it by name; leaving out a term changes the function you're calculating.

Hints

Hint 1
In function notation, the number inside $g(10)$ is the input. You put it into the rule; you don't multiply $g$ by it. How many copies of $x$ need to be replaced?
Hint 2
The rule has two factors, the expressions being multiplied. Keep the plus sign in the first factor and the minus sign in the second. What does each factor look like after you replace $x$ ?

Step-by-step

Substitute and evaluate in Desmos
Step 1
Replace every copy of the input
The input in $g(10)$ is $10$ , so substitute $10$ for every $x$ , not only the first one:
$g(10)=(10+0.2(10))(60-2(10)).$
In particular, $0.2x$ becomes $0.2(10)$ , not $0.2$ .
Step 2
Find the output
Type $g(x)=(x+0.2x)(60-2x)$ in Desmos, then type $g(10)$ on the next line. Desmos prints $480$ . That's the output of the whole product when the input is $10$ . So $g(10)=480$ . Choice C.

Question 734·Easy·Math

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Step-by-step

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