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2 years ago

Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?

Mathematics

2 answers:

Alexandra [31]2 years ago

8 0

Answer:

On a coordinate plane, an exponential function increases in

quadrant 3 into quadrant 4 and approaches y = 0. It goes through

(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25) ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The function $f(x)=\frac{1}{4}(8)^{x}$ is reflected across the

y-axis and then across the x- axis

- Lets revise the reflection of a function across the axes

- If the function f(x) reflected across the x-axis, then the new function

h(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new function

g(x) = f(-x)

∵ $f(x)=\frac{1}{4}(8)^{x}$ is reflected across the y-axis

- Change the sign of x

∴ Its image is g(x) where $g(x)=\frac{1}{4}(8)^{-x}$

∵ $g(x)=\frac{1}{4}(8)^{-x}$ is reflected across the x-axis

- Change the sign of y

∴ Its image is h(x) where $h(x)=-\frac{1}{4}(8)^{-x}$

∴ h(x) is the image of f(x) after reflected across the y-axis then

reflected across the x-axis

* Look to the attached graph for more understand

- f(x) represented by red

- g(x) represented by blue

- h(x) represented by green

* From the graph

- The green graph is in the 3rd and 4th quadrants

- Approaches y = 0 (x-axis)

- point (-1 , -2) lies on it

- It cross the y-axis at point (0 , -0.25)

∴ The answer is the last one

On a coordinate plane, an exponential function increases in

quadrant 3 into quadrant 4 and approaches y = 0. It goes through

(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25)

ycow [4]2 years ago

7 0

Answer:

On a coordinate plane, an exponential function increases in

quadrant 3 into quadrant 4 and approaches y = 0. It goes through

(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25) ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The function is reflected across the

y-axis and then across the x- axis

- Lets revise the reflection of a function across the axes

- If the function f(x) reflected across the x-axis, then the new function

h(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new function

g(x) = f(-x)

∵ is reflected across the y-axis

- Change the sign of x

∴ Its image is g(x) where

∵ is reflected across the x-axis

- Change the sign of y

∴ Its image is h(x) where

∴ h(x) is the image of f(x) after reflected across the y-axis then

reflected across the x-axis

* Look to the attached graph for more understand

- f(x) represented by red

- g(x) represented by blue

- h(x) represented by green

* From the graph

- The green graph is in the 3rd and 4th quadrants

- Approaches y = 0 (x-axis)

- point (-1 , -2) lies on it

- It cross the y-axis at point (0 , -0.25)

∴ The answer is the last one

On a coordinate plane, an exponential function increases in

quadrant 3 into quadrant 4 and approaches y = 0. It goes through

(negative 1, negative 2) and crosses the y-axis at (0, negative 0.25)

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Alex17521 [72]

Answer:

In the long run cost of the refrigerator g(x) will be cheaper.

Step-by-step explanation:

The average annual cost for owning two different refrigerators for x years is given by two functions

f(x) = $\frac{850+62x}{x}$

= $\frac{850}{x}+62$

and g(x) = $\frac{1004+51x}{x}$

= $\frac{1004}{x}+51$

If we equate these functions f(x) and g(x), value of x (time in years) will be the time by which the cost of the refrigerators will be equal.

At x = 1 year

f(1) = 850 + 62 = $912

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So initially f(x) will be cheaper.

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$\frac{850}{x}+62$ = $\frac{1004}{x}+51$

$\frac{1004}{x}-\frac{850}{x}=1004-850$

$\frac{154}{x}=11$

x = $\frac{154}{11}=14$

Now f(15) = 56.67 + 62 = $118.67

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This tells below 14 years f(x) will be less g(x) but after 14 years cost g(x) will be cheaper than f(x).

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Answer: See explanation

Step-by-step explanation:

Based on the scenario in the question, the expression to calculate the number of boxes of sugar Alonso can buys will be:

= 2.75 + 11.50S ≤ 55

When solved further, this will be:

2.75 + 11.50S ≤ 55

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If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (s circle t) (negative 7)?

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Answer:

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Step-by-step explanation:

(s circle t) (negative 7) is a notation for a compound function.

A compound function is a function that has as an argument another function.

Another notation for this compound function is s(t(-7)), that is, the result of the function t(-7) is the value that will be used in the function s(x).

So, first we calculate the value of t(-7):

t(x) = 3x

t(-7) = 3*(-7) = -21

Now, we apply this value for s(x):

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Mariana [72]

Answer:

Fredrick's recipe will make 10 whole loaves.

There will be less flour left over if Frederick's recipe is used.

Step-by-step explanation:

Fredrick and Kate have 17 1/3 cups of flour. They want to make loaves of banana bread for a bake sale. Fredrick has a recipe for banana bread that calls for 1 5/8 cups of flour. Kate has a recipe that calls for 1 3/4 cups of flour. Select all the statements that are true about the recipes.

1. Fredrick's recipe will make 10 whole loaves.

2. Kate's recipe will make 11 whole loaves.

3. There will be less flour left over if Frederick's recipe is used.

4. There will be less flour left over if Kate's recipe is used.

5. More loaves of bread can be made using Frederick's recipe than Kate's recipe.

Solution:

Total cups of flour = 17 1/3

Fredrick recipe = 1 5/8 cups of flour

Kate = 1 3/4 cups of flour

Number of banana bread made with Fredrick's recipe = Total flour / flour per Fredrick's recipe

= 17 1/3 ÷ 1 5/8

= 52/3 ÷ 13/8

=52/3 × 8/13

= 416 / 39

= 10.67 loaves of banana bread

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= 52/3 ÷ 7/4

= 52/3 × 4/7

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Fredrick's recipe will make 10 whole loaves.

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