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Compute the difference quotient $\frac{f(x+h)-f(x)}{h}, \quad h \neq 0$ Whenever possible, simplify the expression so that the resulting expression is defined when $h=0$.$f(x)=m x+b$

$$m$$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Missouri State University

McMaster University

Harvey Mudd College

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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Compute the difference quo…

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Find and simplify the diff…

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Assume $h \neq 0 .$ Comput…

for this problem. We've been given a function f of X equals M x plus B, which you might recognize as ah, line is the linear equation slope intercept form. Now for this problem, we're going to compute the difference quotient of f times X plus H minus F of X over H. This is a, uh, something you're going to see over and over again in calculus. So let's evaluate this difference question using our function f Now, remember, when you see something like F of X plus H, that means we're going to our F function. We're going to substitute X plus H in everywhere we see an X in our original function. So for that first piece, I'm gonna end up with em Times X plus H plus be substituted X plus H in for my ex. I'm going to subtract ffx, which is MX plus B. Remember, we're subtracting that entire piece. You have to make sure you put that f of X value in parentheses so we can distribute the negative sign and it's all over H. Let's get rid of our parentheses and see what we can simplify. We have m X plus m H plus B minus MX minus B over H. So I have some things in common. Positive MX negative mx of a positive be in a negative b. So when I have left, when I've done simplified, my numerator is m h over H and even those h is there going to cancel, which just leaves me with a value of em.

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