Question 805·Easy·Math

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The function $g$ is defined by $g(t) = 4t^2 + 3$ . What is the value of $g(-2)$ ?

Your answer

A function evaluation gives you an input and asks for the output. The number inside $g(-2)$ is the input, so replace the function’s variable with that whole number, then evaluate the rule in Desmos. Keep parentheses around a negative input: $(-2)^2$ is positive, while $-2^2$ is negative.

Hints

Hint 1
In function notation, $g(-2)$ means use $-2$ wherever the rule has $t$ . The entire input goes in parentheses. What expression do you get when you replace $t$ ?
Hint 2
An exponent tells you what to square before you multiply. In $4(-2)^2$ , the negative input is squared, but the $4$ stays outside the square. You can define $g$ in Desmos and enter $g(-2)$ to evaluate it.

Step-by-step

Substitute, then evaluate in Desmos
Step 1
Replace the input in the rule
$g(-2)$ means put $-2$ wherever the rule has $t$ . Replace it with the whole input in parentheses:
$g(-2)=4(-2)^2+3$
The parentheses make the square apply to $-2$ , not only to $2$ .
Step 2
Read the output from Desmos
Type $g(t)=4t^2+3$ , then $g(-2)$ on the next line. Desmos shows $19$ : it squares the negative input before multiplying by $4$ and adding $3$ . So the output for input $-2$ is $19$ . Grid in 19.

Question 805·Easy·Math

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Hints

Step-by-step

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