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Anna35 [415]
3 years ago
5

Graph for f(x)=6^6 and f(x)=14^x

Mathematics
1 answer:
zlopas [31]3 years ago
5 0

Graph Transformations

There are many times when you’ll know very well what the graph of a

particular function looks like, and you’ll want to know what the graph of a

very similar function looks like. In this chapter, we’ll discuss some ways to

draw graphs in these circumstances.

Transformations “after” the original function

Suppose you know what the graph of a function f(x) looks like. Suppose

d 2 R is some number that is greater than 0, and you are asked to graph the

function f(x) + d. The graph of the new function is easy to describe: just

take every point in the graph of f(x), and move it up a distance of d. That

is, if (a, b) is a point in the graph of f(x), then (a, b + d) is a point in the

graph of f(x) + d.

As an explanation for what’s written above: If (a, b) is a point in the graph

of f(x), then that means f(a) = b. Hence, f(a) + d = b + d, which is to say

that (a, b + d) is a point in the graph of f(x) + d.

The chart on the next page describes how to use the graph of f(x) to create

the graph of some similar functions. Throughout the chart, d > 0, c > 1, and

(a, b) is a point in the graph of f(x).

Notice that all of the “new functions” in the chart di↵er from f(x) by some

algebraic manipulation that happens after f plays its part as a function. For

example, first you put x into the function, then f(x) is what comes out. The

function has done its job. Only after f has done its job do you add d to get

the new function f(x) + d. 67Because all of the algebraic transformations occur after the function does

its job, all of the changes to points in the second column of the chart occur

in the second coordinate. Thus, all the changes in the graphs occur in the

vertical measurements of the graph.

New How points in graph of f(x) visual e↵ect

function become points of new graph

f(x) + d (a, b) 7! (a, b + d) shift up by d

f(x) Transformations before and after the original function

As long as there is only one type of operation involved “inside the function”

– either multiplication or addition – and only one type of operation involved

“outside of the function” – either multiplication or addition – you can apply

the rules from the two charts on page 68 and 70 to transform the graph of a

function.

Examples.

• Let’s look at the function • The graph of 2g(3x) is obtained from the graph of g(x) by shrinking

the horizontal coordinate by 1

3, and stretching the vertical coordinate by 2.

(You’d get the same answer here if you reversed the order of the transfor-

mations and stretched vertically by 2 before shrinking horizontally by 1

3. The

order isn’t important.)

74

7:—

(x) 4,

7c’

‘I

II

‘I’

-I

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Help me guys :(<br>i need your help, please....!!!?​
agasfer [191]

Answer:

I think it is B!!

Step-by-step explanation:

5 0
3 years ago
What is equivalent to 2/5?
zhuklara [117]
As in decimal it would be 0.4 but if you want a fraction it could be 4/10

3 0
3 years ago
Choose the word that makes the sentence true. The first digit in the quotient 1,875 ÷9
motikmotik

Hi, I'm Jenny from ExperimentsDIYS and I'm here to help you with your math! :)

I am assuming that you need help with question #1 so we will proceed with that one.

Lets first divide 1,875 ÷ 9.

Using a calculator, this is equal to 208.333333333

We can simplify this number by rounding up.

208.33 would be your answer rounded.

The first digit in this quotient ( Which is the answer to a division problem) is using place value.

The decimal place value chart is attached.

The first digit will be in the hundreds place because it is on the left side of the decimal point.

We are ecstatic to help and if there are any more problems or if we got any answers wrong please tell us! Thank you <3

-ExperimentsDIYS



3 0
3 years ago
An actor gained 20 pounds for a part and then loses 15 pounds during the filming of the movie to go along with the story describ
Tom [10]

We are given statement " gained 20 pounds and loses 15 pounds".

<em>Note: We take plus or positive sign for gain word and we take minus or negative sign for the loses word.</em>

Gained 20 means +20.

Loses 15 mean -15.

Therefore, we can setup an expression as:

<h3>+20 -15.</h3>

20 is a positive number and 15 is a negative number.

Because we have opposite signs of numbers, we would subtract them.

20-15 = 5 pounds.


6 0
3 years ago
Hurry Please
sleet_krkn [62]
It would be true no explanation needed
4 0
3 years ago
Read 2 more answers
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