Evaluating Functions

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Do curso por University of California, Irvine

Pre-Calculus: Functions

311 classificações

University of California, Irvine

Pre-Calculus: Functions

311 classificações

This course covers mathematical topics in college algebra, with an emphasis on functions. The course is designed to help prepare students to enroll for a first semester course in single variable calculus. Upon completing this course, you will be able to: 1. Solve linear and quadratic equations 2. Solve some classes of rational and radical equations 3. Graph polynomial, rational, piece-wise, exponential and logarithmic functions 4. Find integer roots of polynomial equations 5. Solve exponential and logarithm equations 6. Understand the inverse relations between exponential and logarithm equations 7. Compute values of exponential and logarithm expressions using basic properties

Na lição

Functions. Graphs of Functions. Transformations of Functions.

In this module, we define the notion of "function". We learn to distinguish between functions and non-functions in graphical, symbolic and tabular form. Finally, we will explore graphs of functions and how these graphs behave under linear transformations.

Introduction to Functions & Graphs 13:23

Relations versus Functions 5:01

Functions and the Vertical Line Test 5:40

Evaluating Functions 6:13

Conheça os instrutores

Dr. Sarah Eichhorn
Associate Dean, Distance Learning & Tenured Lecturer
Dr. Rachel Cohen Lehman

[SOUND] Let's look at Evaluating Functions. [SOUND] For example, if f and

g are defined as follows let's find all four of these, f(-2), f(x^2), g(3).

And g(x+1). Now, we're given that f(x) = 2 - 3x +

x^2. So when we are evaluating this function

at any input, we put the input here, and here.

Lets write that out. So we have f of any input.

Is equal to 2 - 3 times that input + that input squared.

Now, what about the function g? We're given that g(x) = x + 4 / 2x - 1.

So when we are evaluating g at any input, we put the input here as well as here.

So, let's write that out as well. Namely, g of any input, is = to that

input. Plus 4 divided by 2 times that input, and

then minus 1. Alright, so we're first asked to find

f(-2). Which means that this -2 here is our

input. Which means we put it over here, and

here. That is, this is equal to 2 - 3 * this

input. -2 + that input, or (-2)^2.

Which is equal, to 2 + 6 + 4 or 12, which should be our answer to the first part.

All right. What about f(x^2)?

Now, don't let it confuse you that this is a variable now.

And moreover, that it's the same variable x that we see up here in the definition

of our function. Remember, what ever is inside these

parenthesis is our input. Which means, we need to put it in over,

and here. That is this is = 2-3 * that input, or *

x^2 + that input, or x^2. Quantity ^2, which is =.

2 - 3x^2 + x^4. which would be our answer to the second

part. All right, what about this third one

here, g of 3? Now we'll start working with our function g.

So 3 then is going to be our input. Which means looking here on the right,

we're going to plug it in here and we're going to plug it in here.

That is, this is equal to the input which is 3.

+ 4 / 2 times the input or 2 * 3 - 1, which is equal to, 7 / 6 - 1, which is 5,

which would be our answer to the third part.

And finally, what about g(x+1)? Again, don't let it confuse you, that you see a

variable, here, inside the parentheses. And moreover, that it's the same

variable, as we have up here, in the definition of g.

Remember, whatever is inside the parenthesis is our input.

So this whole quantity, x + 1, is our input.

Which means over here on the right, we're going to plug it in here, and here.

Namely, this is equal to the input, or x + 1 + 4 / 2 * the input, or 2 * x + 1 and

then - 1, which = x + 5 / now distributing our 2, we have 2x + 2 - 1,

which is equal to x + 5 / 2x + 1. Which would be our last answer.

And this is how we evaluate functions. Whatever we see inside the parenthesis,

we put in as our input. Thank you and we'll see you next time.

[SOUND]

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