Question 746·Easy·Math

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$g(x)=2^x+1$

Which table gives three values of $x$ and their corresponding values of $g(x)$ for the given function $g$ ?

$x$	0	1	3
$g(x)$	1	2	8

$x$	0	1	3
$g(x)$	3	5	17

$x$	0	1	3
$g(x)$	2	3	9

$x$	0	1	3
$g(x)$	3	4	10

A table of inputs and outputs calls for function evaluation: put each listed $x$ into the given rule to find its matching $g(x)$ . On a timed test, define the rule once in Desmos and evaluate the inputs shown in the tables. Watch for a number added outside the exponent; it changes every output.

Hints

Hint 1
A function value such as $g(0)$ is the output when the input is $0$ . Every table lists $x=0$ , so start there: that one input makes the exponent quick to check.
Hint 2
An exponent tells you how many copies of the base to multiply. Calculate the power first, then add the number outside the exponent. How can you check the outputs against all three inputs in a table?

Step-by-step

Evaluate the table inputs
Step 1
Use the easiest input first
Every table lists $x=0$ . A zero exponent makes a nonzero base equal $1$ , so $2^0=1$ . Start with a shared input that makes the rule quick to evaluate. Don't treat $2^0$ as $0$ .
Step 2
Find the matching outputs
Type $g(x)=2^x+1$ , then $g(0)$ , $g(1)$ , and $g(3)$ on separate lines. Desmos shows $2$ , $3$ , and $9$ . The $+1$ is added after the power, so each output must sit under its own input: $2$ under $0$ , $3$ under $1$ , and $9$ under $3$ . The table with those values matches the function. Choice C.

Question 746·Easy·Math

Strategy

Hints

Step-by-step

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