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

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 52 | Free SAT Prep | Aniko

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Question 52·Easy·Nonlinear Functions

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$p(x)=2x^2-3$

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

$x$	0	1	2
$p(x)$	-3	-1	6

$x$	0	1	2
$p(x)$	-1	-1	5

$x$	0	1	2
$p(x)$	-3	-2	5

For function-value questions like this, ignore the tables at first and go straight to the formula: plug each given x-value into the function carefully using the correct order of operations (square, then multiply, then add/subtract). Once you have the exact outputs (like $p(0)$ , $p(1)$ , $p(2)$ ), quickly scan the answer choices and eliminate any table that has even one mismatched value; there is no need to compute anything for the wrong tables themselves.

Hints

Click me!

Use the definition of the function

You are given $p(x)=2x^2-3$ . To find $p(0)$ , $p(1)$ , and $p(2)$ , plug each of these x-values into the expression and simplify.

Start with x = 0

What do you get when you substitute $x=0$ into $2x^2-3$ ? Remember that $0^2=0$ , and then follow the order of operations.

Then try x = 1 and x = 2

After you find $p(0)$ , repeat the same steps for $x=1$ and $x=2$ . Once you have all three values, compare them to the $p(x)$ rows in each table and see which one matches exactly.

Desmos Guide

Enter the function into Desmos

In Desmos, type p(x)=2x^2-3 on a new line so that Desmos defines the function $p(x)$ and shows its graph.

Create a table of values

Click the "+" icon and choose "Table", then in the x-column enter 0, 1, and 2. In the y-column, type p(x) so Desmos automatically fills in the corresponding $p(x)$ values for each x.

Compare with the answer choices

Look at the $p(x)$ values in your Desmos table for $x=0,1,2$ and then choose the answer option whose $p(x)$ row matches all three of those values exactly.

Step-by-step Explanation

Understand what the function notation means

The function is defined by $p(x)=2x^2-3$ .

This means: for any input $x$ , you first square $x$ , then multiply by 2, and finally subtract 3. You need to do this for $x=0$ , $x=1$ , and $x=2$ .

Evaluate the function at x = 0

Compute $p(0)$ by substituting $x=0$ into the formula:

p(0)=2(0)^2-3=2\cdot 0-3=0-3=-3

So, any correct table must have $-3$ in the $p(x)$ row under $x=0$ .

Evaluate the function at x = 1 and x = 2

Now substitute $x=1$ :

p(1)=2(1)^2-3=2\cdot 1-3=2-3=-1

Then substitute $x=2$ :

p(2)=2(2)^2-3=2\cdot 4-3=8-3=5

So the three ordered pairs should be $(0,-3)$ , $(1,-1)$ , and $(2,5)$ for $(x,p(x))$ .

Match your results to the correct table

Look at each answer choice and check the $p(x)$ row for $x=0,1,2$ .

The only table whose $p(x)$ values are $-3$ when $x=0$ , $-1$ when $x=1$ , and $5$ when $x=2$ is:

$x$	0	1	2
$p(x)$	-3	-1	5

So this table (choice D) is the correct answer.

Study Hints

Hints

Click me!

Use the definition of the function

You are given $p(x)=2x^2-3$ . To find $p(0)$ , $p(1)$ , and $p(2)$ , plug each of these x-values into the expression and simplify.

Start with x = 0

What do you get when you substitute $x=0$ into $2x^2-3$ ? Remember that $0^2=0$ , and then follow the order of operations.

Then try x = 1 and x = 2

After you find $p(0)$ , repeat the same steps for $x=1$ and $x=2$ . Once you have all three values, compare them to the $p(x)$ rows in each table and see which one matches exactly.

Desmos Guide

Enter the function into Desmos

In Desmos, type p(x)=2x^2-3 on a new line so that Desmos defines the function $p(x)$ and shows its graph.

Create a table of values

Click the "+" icon and choose "Table", then in the x-column enter 0, 1, and 2. In the y-column, type p(x) so Desmos automatically fills in the corresponding $p(x)$ values for each x.

Compare with the answer choices

Look at the $p(x)$ values in your Desmos table for $x=0,1,2$ and then choose the answer option whose $p(x)$ row matches all three of those values exactly.

Step-by-step Explanation

Understand what the function notation means

The function is defined by $p(x)=2x^2-3$ .

This means: for any input $x$ , you first square $x$ , then multiply by 2, and finally subtract 3. You need to do this for $x=0$ , $x=1$ , and $x=2$ .

Evaluate the function at x = 0

Compute $p(0)$ by substituting $x=0$ into the formula:

p(0)=2(0)^2-3=2\cdot 0-3=0-3=-3

So, any correct table must have $-3$ in the $p(x)$ row under $x=0$ .

Evaluate the function at x = 1 and x = 2

Now substitute $x=1$ :

p(1)=2(1)^2-3=2\cdot 1-3=2-3=-1

Then substitute $x=2$ :

p(2)=2(2)^2-3=2\cdot 4-3=8-3=5

So the three ordered pairs should be $(0,-3)$ , $(1,-1)$ , and $(2,5)$ for $(x,p(x))$ .

Match your results to the correct table

Look at each answer choice and check the $p(x)$ row for $x=0,1,2$ .

The only table whose $p(x)$ values are $-3$ when $x=0$ , $-1$ when $x=1$ , and $5$ when $x=2$ is:

$x$	0	1	2
$p(x)$	-3	-1	5

So this table (choice D) is the correct answer.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation