Question 554·Easy·Math

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The function $p$ is defined by $p(x)=\sqrt{49 - x^2}$ . What is the value of $p(0)$ ?

A known input in function notation means you evaluate the rule: replace every $x$ with the number in parentheses. Define the function in Desmos, then enter the requested value to check your substitution. With a square root, watch the sign: the square-root symbol returns the nonnegative value, even though a positive and a negative number can have the same square.

Hints

Hint 1
The number inside $p(0)$ is the input. To evaluate a function, replace every $x$ in its rule with that number. What does the squared term become?
Hint 2
A square root asks for the nonnegative number whose square is the number underneath. Both a positive and a negative number might have that square, but which one does the symbol return?

Step-by-step

Substitute, then evaluate in Desmos
Step 1
Put the input into the rule
In function notation, $p(0)$ means use $0$ as the input, so replace $x$ with $0$ :
$p(0)=\sqrt{49-0^2}.$
Step 2
Simplify under the square root
Square $0$ and subtract it from $49$ : $p(0)=\sqrt{49}$ . The square root sign returns only the nonnegative number whose square is $49$ , not both a positive and a negative number.
Step 3
Read the output
Type $p(x)=\sqrt{49-x^2}$ in Desmos, then type $p(0)$ . Desmos shows $7$ . Since $7^2=49$ and $7$ is nonnegative, the function's output at input $0$ is $7$ . Choice B.

Question 554·Easy·Math

Strategy

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