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3 years ago

The graph is a transformation of one of the basic functions. Find the equation that defines the function.

Mathematics

2 answers:

nikdorinn [45]3 years ago

8 0

Answer:

$y = 5-\sqrt{x}$

Step-by-step explanation:

Note that the graph shown is a transformation of the parent function

$y = \sqrt{x}$

The main function cuts the x-axis at x = 0 and has no negative values of y. In addition, the main function is always growing.

Note that the function shown is decreasing and intercepts the y-axis at y = 5.

Therefore, the graph of the main function has been reflected on the x-axis and displaced 5 units upwards.

If we do y = f(x) then to reflect the main function on the x-axis and move it upwards 5 units we make the following transformation

$y = -f(x) + 5$ .

Then the graphed function is:

$y = 5-\sqrt{x}$

SCORPION-xisa [38]3 years ago

6 0

Answer:

f(x) = -logx + 4.

Step-by-step explanation:

y = -log x approaches the point (0, 1) but this approaches (0, 5)

Looks like the graph of - log x + 4.

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Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it t

Dmitry [639]

Answer:

Levi's dad takes 1.67 hours to wash the car by himself

Step-by-step explanation:

* Lets explain how to solve the problem

- Levi takes 2.5 hours to wash his dad's car alone

- Levi and his dad take 1 hour to wash the dad's car together

∵ Levi takes 2.5 hours to wash the car alone

∴ The rate of Levi is 1/2.5 car/hr

∵ His dad takes x hours to wash the car alone

∴ The rate of his dad is 1/x car/hr

∵ They working together for 1 hour to wash the car

- The equation of the work is rate of Levi × t + rate of his dad × t = 1

∵ t is the time of working together

∵ t = 1 hour

∴ $\frac{1}{2.5}(1)+\frac{1}{x}(1)=1========\frac{1}{2.5}+\frac{1}{x}=1$

- Multiply both sides by 2.5x to cancel the denominators

∵ $\frac{1}{2.5}(2.5x)=x=====\frac{1}{x}(2.5x)=2.5$

∵ 1 × (2.5x) = 2.5x

∴ x + 2.5 = 2.5x

- Subtract x from both sides

∴ 2.5 = 1.5x

- Divide both sides by 1.5

∴ x = 5/3 ≅ 1.67

∵ x is the the time of his dad to wash the car alone

∴ Levi's dad takes 1.67 hours to wash the car by himself

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