Question 738·Medium·Math

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The table shows several values of $x$ and their corresponding values of $f(x)$ for the function $f(x) = 7(3)^{x-2} - 4$ .

$x$	$f(x)$
2	3
3	17
4	$c$

In the table, $c$ is a constant. What is the value of $c$ ?

A table with a given exponential function and a missing output is asking you to evaluate the rule, not find a pattern from the other rows. Use the missing row’s input: define the function in Desmos, then evaluate it there. Keep the entire rule, including the number subtracted after the power.

Hints

Hint 1
In function notation, $f(4)$ means the output when the input is $4$ . Look at the row with the missing output. What function value does that make $c$ ?
Hint 2
The entire exponent is $x-2$ . Put the missing row’s input in place of $x$ , and keep the $-4$ outside the power when you evaluate.

Step-by-step

Evaluate the given function
Step 1
Identify the output the table needs
The missing entry is in the row where $x=4$ . In function notation, $f(4)$ means the output at that input, so use the row’s $x$ -value as the input to the given rule: $c=f(4)$ .
Step 2
Put the input into the rule
Replace $x$ with $4$ , including in the entire exponent $x-2$ : $f(4)=7(3)^{4-2}-4$ . The $-4$ is outside the power, so it still gets subtracted after the multiplication.
Step 3
Read the missing output
Type the function into Desmos, then type $f(4)$ on the next line. Desmos shows $59$ . That's the full output for the row where $x=4$ , so $c=59$ . Choice C.

Question 738·Medium·Math

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