Question 497·Easy·Algebra

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The function $f$ is defined by $f(x)=kx+12$ , where $k$ is a constant. If $f(6)=0$ , what is the value of $k$ ?

An unknown constant, a number that stays fixed, can be found from one input-output pair. Replace the input variable with the number in parentheses, then set the rule equal to the stated output. Type that equation as a Desmos regression, an entry using $\sim$ to find the unknown. The number in parentheses is the input, not the output.

Hints

Hint 1
In function notation, the number in parentheses is the input you put in, and the number after $=$ is the output you get back. Replace $x$ with the input, not the output, to build your equation.
Hint 2
After substitution, the equation has only one unknown: $k$ . A Desmos regression can find that constant. Type the equation with $\sim$ in place of $=$ , then read the value under PARAMETERS.

Step-by-step

Substitute, then find the constant
Step 1
Turn the function value into an equation
The input in $f(6)=0$ is $6$ , and the output is $0$ . So replace $x$ with $6$ in the given rule and set it equal to $0$ : $6k+12=0$ . Don't replace $x$ with $0$ ; that would use the output as the input.
Step 2
Find the value of the constant
Type $6k+12\sim0$ in Desmos. The regression sign $\sim$ asks Desmos to find the value of $k$ that makes the equation true. Under PARAMETERS, it shows $k=-2$ . So the constant is $-2$ . Choice C.

Question 497·Easy·Algebra

Strategy

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Step-by-step

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Strategy

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