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Flashcards: Working with Function Notation

$\displaystyle f(x)=x^2-x$

The function $\displaystyle f$ is defined above. What is $\displaystyle f(9)-f(7)$?

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Flashcards: Working with Function Notation

$\displaystyle f(x)=x^2-x$

The function $\displaystyle f$ is defined above. What is $\displaystyle f(9)-f(7)$?

Report an Error Copyright Notice

Flashcards: Working with Function Notation

$\displaystyle f(x)=x^2-x$

The function $\displaystyle f$ is defined above. What is $\displaystyle f(9)-f(7)$?

Your answer:

Correct answer:

Explanation:

When you're given the definition of a function as you are here, $\displaystyle f(x)=x^2-x$, your job to calculate a function is to take the value in parentheses and plug that in for $\displaystyle x$ wherever it appears in the definition. Here, qualitatively, you're being told "whatever $\displaystyle x$ is, square it and then subtract $\displaystyle x$ from that square." That means that:

$\displaystyle f(9)=9^2-9$

So:

$\displaystyle f(9)=81-9=72$

And for f(7) $\displaystyle f(7)$ you'd have:

$\displaystyle f(7)=7^2-7$

So:

$\displaystyle f(7)=49-7=42$

This means that $\displaystyle f(9)-f(7)=72-42=30$, so the correct answer is $\displaystyle 30$.

Flashcards: Working with Function Notation

If $f(x)=\frac{x^3-2x^2+3x+1}{x}$ $\displaystyle f(x)=\frac{x^3-2x^2+3x+1}{x}$, what is f(-1) $\displaystyle f(-1)$?

-5

-1

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Flashcards: Working with Function Notation

If $f(x)=\frac{x^3-2x^2+3x+1}{x}$ $\displaystyle f(x)=\frac{x^3-2x^2+3x+1}{x}$, what is f(-1) $\displaystyle f(-1)$?

Your answer:

-5

Your answer:

-1

Correct answer:

Explanation:

Whenever you're working with a function f(x)= $\displaystyle f(x)=$ with an algebraic definition like the one you're given, your job is to plug in the value (in this case $\displaystyle -1$) wherever $\displaystyle x$ appears in that definition. This means that your work should look like:

$f(-1)=\frac{(-1)^3-2(-1)^2+3(-1)+1)}{-1}$ $\displaystyle f(-1)=\frac{(-1)^3-2(-1)^2+3(-1)+1)}{-1}$

The key here becomes keeping the negative/positive signs in place given all the addition/subtraction and multiplication of negatives in the numerator. Once you've applied the exponents and multiplication in the numerator, you should have:

$\frac{-1-2-3+1}{-1}$ $\displaystyle \frac{-1-2-3+1}{-1}$

This then simplifies to $\frac{-5}{-1}$ $\displaystyle \frac{-5}{-1}$, in which the negatives in numerator and denominator cancel, leaving you with just $\displaystyle 5$ as your answer.

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Flashcards: Working with Function Notation

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Flashcards: Working with Function Notation

Flashcards: Working with Function Notation

Flashcards: Working with Function Notation

Flashcards: Working with Function Notation

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Flashcards: Working with Function Notation

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Flashcards: Working with Function Notation

Flashcards: Working with Function Notation

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