1. ## Simplifying Expressions

How would simplify this? I can't seem to get the right answer.

For the function f(x)=x^2−7x, simplify each expression as much as possible.

1) (f(x+h) - f(x)) / h :h cannot = 0

and 2) (f(w) - f(x)) / w - x :x cannot = w

2. Have you at least tried to evaluate $f(x + h)$?

3. Sadly i don't know how to even go about that. Since h has no defined statement, would i just leave it as the variable h? So would that turn into (x^2 -7x +h) - (x^2 - 7x) and then the x^2's and the 7x's would cancel out and i would be left with just h?

4. Replace each $x$ in $f(x)$ with $x + h$.

5. (x+h)^2 - 7(x+h) => (x^2 + h^2 +2hx) - (7x+h)

Like this?

6. Yes, and you can simplify it further.

Then evaluate $f(x + h) - f(x)$.

Then evaluate $\frac{f(x +h) - f(x)}{h}$.

7. So now i have x^2 + h^2 - 5hx / h. How can i simplify this further?

8. Check your simplification of $f(x + h) - f(x)$ again. Each term should have an $h$ in it.

9. I don't see it. How would you end up with a h in the x^2 term?

10. $f(x + h) - f(x) = (x^2 + 2xh + h^2 - 7x - 7h) - (x^2 - 7x)$

$= 2xh + h^2 - 7h$.

So what do you think $\frac{f(x+h)-f(x)}{h}$ is?

11. Would you divide out h? so you would be left with 2x + h -7. Would i isolate h to leave 7 - 2x?

12. Yes, divide everything by $h$. So the first thing you wrote is correct.

13. What would i do next? Since i am not allowed to have an h in my answer.

14. Why can't you keep an $h$ in your answer? All you've been told is that $h \neq 0$...

15. If i enter an answer with h in it it prompts me saying that i cannot have an h.

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