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pychu [463]
3 years ago
7

How can you use transformations to graph this function?

Mathematics
2 answers:
valentina_108 [34]3 years ago
8 0

Answer:

Sketch the graph of y=7^x

Reflect the graph across the y-axis to show the function y=7^-x

Stretch the graph vertically by a factor of 3 to show the function y= 3*7^-x

Shift the graph up 2 units to show the function y=3*7^-x+2

Step-by-step explanation:

tatuchka [14]3 years ago
7 0
The parent function for this function is 

f(x)=  7^{x}

We have to explain how the given function can be obtained from the parent function.

Let y=g(x)

So, 

g(x)=3*7^{-x} +2

Notice that x in the exponent is multiplied by -1. Multiplying x by -1 implies the reflection of the graph across y-axis.

The function value is multiplied by 3. This suggest a vertical expansion by a factor of 3.

2 is being added to the function value, this implies a vertical shift upwards by 2 units.

So, we can write:

y = g(x) = 3f(-x) + 2

Thus following translations are applied:

a) Reflection across y-axis
b) Vertical stretch by a factor of 3
c) Upward shift by 2 units
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The safety instructions for a 20 foot ladder say the ladder should not be inclined more than 70 degrees with the ground. suppose
Romashka [77]

Answer: the distance of the base of the house to the foot of the ladder is 6.84 feet

Step-by-step explanation:

The scenario is shown in the attached photo.

Right angle triangle ABC is formed when the ladder leans against the wall of the house.

AC = the height of the ladder

AB = x feet = distance of the base of the house to the foot of the ladder

BC is the wall of the building.

To determine x, we will apply trigonometric ratio

Cos # = adjacent/hypotenuse

Where

# = 70 degrees

Hypotenuse = 20

Adjacent = x

Cos 70 = x/20

x = 20cos70

x = 20 × 0.3420

x = 6.84 feets

4 0
3 years ago
A turtle walks 12 feet in one hour. How many inches does the turtle walk in one hour?
blagie [28]
144 inches. 12 feet in one hour
12 inches per feet

12feet x 12 inches per foot= 144 inches
6 0
2 years ago
If f(x)=x/3 -2 and g(x)=3x^2+2x-6 find (f+g)(x)
umka21 [38]

Answer:

(f + g)(x) = 3x² + (7/3)x - 8

Step-by-step explanation:

To find (f + g)(x), you need to add both the f(x) and g(x) equations together.

f(x) = x/3 - 2 ..... which is equal to ... f(x) = (1/3)x - 2

g(x) = 3x² + 2x - 6

(f + g)(x) = ((1/3)x - 2) + (3x² + 2x - 6)          <----- Add both equations

(f + g)(x) = 3x² + (1/3)x + 2x - 2 - 6              <----- Rearrange (2 = 6/3)

(f + g)(x) = 3x² + (7/3)x - 8                           <----- Simplify similar terms

6 0
1 year ago
Find the midpoint of the segment with the given endpoints . G(-3,-5) and H(1,-1)
Serhud [2]
All you have to do for this is follow the midpoint formula.

Let me know if the picture is unclear and I'll type it out for you.

4 0
2 years ago
In ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45. What is the value of the cosine of ∠X to the nearest hundredth?
kotegsom [21]

The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.

Step-by-step explanation:

The given is,

                   In ΔWXY, ∠Y=90°

                        XW = 53

                         YX = 28

                        WY = 45

Step:1

             Ref the attachment,

             Given triangle XWY is right angled triangle.

             Trigonometric ratio's,

                              Cos ∅  = \frac{Adj}{Hyp}    

             For the given attachment, the trigonometric ratio becomes,

                              Cos ∅  = \frac{XY}{XW}.....................................(1)

             Let, ∠X = ∅

             Where, XY = 28

                         XW =  53

             Equation (1) becomes,

                                 Cos ∅  = \frac{28}{53}

                                 Cos ∅ = 0.5283

                                        ∅ = cos^{-1} (0.5283)

                                        ∅ = 58.109°

Result:

          The value of ∠X = 58.11°, If ΔWXY, the measure of ∠Y=90°, XW = 53, YX = 28, and WY = 45.

             

4 0
3 years ago
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