Which table gives three values of and their corresponding values of for the given function ?

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 187 | Free SAT Prep | Aniko

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Question 187·Easy·Nonlinear Functions

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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
$g(x)$	3	4	10

When a question asks which table matches a given function, ignore the choices at first and quickly compute the outputs the function gives for the listed $x$ -values, being careful with order of operations (exponent first, then addition or subtraction). Once you have the correct outputs, scan the tables for an exact match on all the corresponding $x$ -values; if even one output is off, eliminate that option and move on. This direct substitution approach is fast and avoids getting distracted by patterns in the answer choices.

Hints

Click me!

Use the definition of the function

$g(x)=2^x+1$ tells you how to get the output from any input $x$ . What should you do with each $x$ -value from the table?

Start with $x=0$

Substitute $x=0$ into $2^x+1$ . Remember that $2^0$ equals $1$ . What does that make $g(0)$ ?

Repeat for $x=1$ and $x=3$

Now plug in $x=1$ and then $x=3$ into $2^x+1$ . Be careful to calculate $2^x$ first and then add $1$ .

Compare your results to the options

Once you know $g(0)$ , $g(1)$ , and $g(3)$ , look for the table whose $g(x)$ row matches all three of your computed values.

Desmos Guide

Enter the function into Desmos

Type y = 2^x + 1 (or g(x) = 2^x + 1) into a new expression line so Desmos knows the function.

Evaluate the function at the given x-values

Either add a table in Desmos with $x$ -values $0$ , $1$ , and $3$ next to the equation, or type separate lines 2^0+1, 2^1+1, and 2^3+1. Read off the three outputs and then choose the table option whose $g(x)$ row matches all three values.

Step-by-step Explanation

Understand what the function means

The function is $g(x)=2^x+1$ . This means: for any input $x$ ,

First compute $2^x$ (2 raised to the $x$ power),
Then add $1$ to that result.

We need to do this for $x=0$ , $x=1$ , and $x=3$ .

Compute $g(0)$

Substitute $x=0$ into $g(x)=2^x+1$ :

g(0)=2^0+1

We know $2^0=1$ , so:

g(0)=1+1=2

So when $x=0$ , $g(x)=2$ .

Compute $g(1)$

Now substitute $x=1$ :

g(1)=2^1+1

We know $2^1=2$ , so:

g(1)=2+1=3

So when $x=1$ , $g(x)=3$ .

Compute $g(3)$ and match the table

Finally, substitute $x=3$ :

g(3)=2^3+1

We know $2^3=8$ , so:

g(3)=8+1=9

So the correct table must show $g(x)$ values $2$ , $3$ , and $9$ for $x=0$ , $1$ , and $3$ , respectively. The only table that does this is:

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

Study Hints

Hints

Click me!

Use the definition of the function

$g(x)=2^x+1$ tells you how to get the output from any input $x$ . What should you do with each $x$ -value from the table?

Start with $x=0$

Substitute $x=0$ into $2^x+1$ . Remember that $2^0$ equals $1$ . What does that make $g(0)$ ?

Repeat for $x=1$ and $x=3$

Now plug in $x=1$ and then $x=3$ into $2^x+1$ . Be careful to calculate $2^x$ first and then add $1$ .

Compare your results to the options

Once you know $g(0)$ , $g(1)$ , and $g(3)$ , look for the table whose $g(x)$ row matches all three of your computed values.

Desmos Guide

Enter the function into Desmos

Type y = 2^x + 1 (or g(x) = 2^x + 1) into a new expression line so Desmos knows the function.

Evaluate the function at the given x-values

Step-by-step Explanation

Understand what the function means

The function is $g(x)=2^x+1$ . This means: for any input $x$ ,

First compute $2^x$ (2 raised to the $x$ power),
Then add $1$ to that result.

We need to do this for $x=0$ , $x=1$ , and $x=3$ .

Compute $g(0)$

Substitute $x=0$ into $g(x)=2^x+1$ :

g(0)=2^0+1

We know $2^0=1$ , so:

g(0)=1+1=2

So when $x=0$ , $g(x)=2$ .

Compute $g(1)$

Now substitute $x=1$ :

g(1)=2^1+1

We know $2^1=2$ , so:

g(1)=2+1=3

So when $x=1$ , $g(x)=3$ .

Compute $g(3)$ and match the table

Finally, substitute $x=3$ :

g(3)=2^3+1

We know $2^3=8$ , so:

g(3)=8+1=9

So the correct table must show $g(x)$ values $2$ , $3$ , and $9$ for $x=0$ , $1$ , and $3$ , respectively. The only table that does this is:

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

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation