Let `f(x) = x^2 - 3x - 7` . Find `f(-3)` .

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txmedteach's profile pic

txmedteach | High School Teacher | (Level 3) Associate Educator

Posted on

To solve this problem, we simply substitute -3 for x in every term for f(x) in the following way:

`f(-3) = (-3)^2 - 3(-3) -7`

Let's simplify. Remember, when you square a negative number, you get a positive result:

`f(-3) = 9 - (-9)-7`

Now, we're subtracting a negative number. This equates to adding a positive number! Let's continue:

`f(-3) = 9 + 9 - 7`

Now, we just add and subtract:

`f(-3) = 18 - 7 = 11`

Therefore, f(-3) = 11. And you're done!

I hope that helps. I could see in this question how you might get caught up in the signs of each term (whether they're negative or positive, whether you add or subtract, or what-have you). Just remember that you multiply first, then add or subtract. Also, if you have difficulty conceptualizing the negatives and positives, you might find it helpful to just memorize the rules associated with them:

Multiplication:

positive * positive = positive

negative * negative = positive

positive * negative = negative

negative * positive = negative

Addition/Subtraction:

Number + positive = number  - negative

Number - positive = number + negative

Hopefully that works for you!

Sources:
Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

This is a simple substitution problem: 

Let  . Find  .

 `f(-3) = (-3)^2 -3(-3) - 7`
`<span style="font-size: 14px;"><br></span>`
`<span style="font-size: 14px;">f(-3) = 9 + 9 - 7</span>`
`<span style="font-size: 14px;"><br data-mce-bogus="1"></span>`
`<span style="font-size: 14px;">f(-3) = 11</span>`
atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

 . Find  

substitute the Xs with -3

f(-3) = -3^2 -3(-3) - 7

simplify

f(-3) = 9 + 9 -7

combine terms

f(-3) = 11

nicole8923's profile pic

nicole8923 | Student, Grade 10 | (Level 1) Salutatorian

Posted on

You would simply substitute -3 for x

IT would then become:

f(-3)=(-3)^2-3(-3)-7

f(-3)=(9)+(9)-7

f(-3)=18-7

f(-3)=11

acompanioninthetardis's profile pic

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

Posted on

F (x)= X^2 -3x-7, and f (-3) 

So you just substitute -3 for the x giving you

(-3^2)-3 (-3)-7

9+9-7

18_7

=11

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