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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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You read 9.75 pages in your science book and 24.5pages of a play for English class. It takes you 1.2minutes to read each page of
drek231 [11]

Answer:

the number of time spend in reading is 31.3 minutes

Step-by-step explanation:

The computation of the number of time spend in reading is as follows:

= 9.75 pages in science book × 1.2 minutes + 24.5 pages in english class × 0.8 minutes

= 11.7 minutes + 19.6 minutes

= 31.3 minutes

Hence, the number of time spend in reading is 31.3 minutes

The same is relevant and considered

6 0
3 years ago
I need help #16 an 17
Romashka [77]
Seventeen is :3 2/2
7 0
3 years ago
Read 2 more answers
NO LINKS AND PLEASE MAKE YOUR ANSWER SIMPLE.
Ber [7]

The student with the correct answer is Dylan who says the decimal should be placed between the 8 and 0.

This is base on the estimation that 3.01 is a two decimal place number, so the product 18.06 should also be in 2 decimal place.

<h3>How to find product of decimal number?</h3>

A decimal number is a number expressed in the decimal system (base 10).

Place value:

  • Ten thousand
  • Thousand
  • Hundred
  • Ten
  • ones
  • . decimal point
  • tenth
  • hundredths
  • thousandth
  • ten thousandth
  • hundred thousandth

6 × 3.01

3.01

  • 3 = ones
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6 × 3.01

= 18.06

Therefore, Lucas is incorrect with his answer that the decimal should be placed between the 1 and 8.

Read more on decimal number:

brainly.com/question/1827193

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5 0
1 year ago
In a class of 34 students, 19 of them are girls.
Colt1911 [192]

Answer:

55.9%

Step-by-step explanation:

To find the percent that are girls, take the number of girls over the total number of students

19/34

.558823529

To change to percent form, multiply by 100%

55.8823529%

To 1 decimal place

55.9%

5 0
3 years ago
Read 2 more answers
Fill in the missing numbers to complete the pattern:<br><br> 5.81, ,5.91,5.96, ,6.06
zimovet [89]
You’re going to be adding by .05

so the first one would be 5.86 and the second one would be 6.01

hopefully this helps!
4 0
3 years ago
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