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Stella [2.4K]
3 years ago
13

1.what is the vertex of the graph? (see attachment)

Mathematics
2 answers:
AfilCa [17]3 years ago
5 0
Hello :
here is a solution :

Sergio039 [100]3 years ago
5 0
1. C. (1,3)
2. A. maximum
3. A. 3
4. C. 42 feet
5. D. 11,-11
6. C. -7,-1
7. C. -6,4
8. A. 3.33 ft
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Graph for f(x)=6^6 and f(x)=14^x
zlopas [31]

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

5 0
3 years ago
Find x <br> Plz help me !!!
mel-nik [20]

Answer:

\Huge\boxed{x=33.2}

Step-by-step explanation:

Hello there!

We can solve for x using law of sines

As we can see in the image a side length divided by sin ( its opposite angle) = a different side length divided by sin ( its opposite angle)

So we can use this equation to solve for x

\frac{21}{sin(35)} =\frac{x}{sin(65)}

Our objective is to isolate the variable using inverse operations so to get rid of sin (65) we multiply each side by sin (65)

\frac{x}{sin(65)} sin(65)=x\\\\\frac{21}{sin(35)} sin(65)=\frac{21sin(65)}{sin(35)}

we're left with

x=\frac{21sin(65)}{sin(35)}\\x=33.18208755

assuming we have to round the answer would be 33.18 or 33.2

7 0
3 years ago
What is the range of the following data set?​
sashaice [31]

Answer:  The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

5 0
3 years ago
Round each number to the nearest hundredth.
Nina [5.8K]
A. 8.75
B. 0.72
C. 9.31
D. 23.04
E. 6.98
5 0
3 years ago
Read 2 more answers
How do the areas of the parallelogram compare?
IrinaK [193]
The first choice is right, area of 1 is 20, area of 2 is 16
5 0
3 years ago
Read 2 more answers
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