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dem82 [27]
3 years ago
15

H(x) = x3 + 7 Determine whether the function is one-to-one.

Mathematics
1 answer:
zubka84 [21]3 years ago
6 0

Answer:

we conclude that the function is one-to-one.

Step-by-step explanation:

A function will a one-to-one function if it

  • passes the vertical line test to make sure it is indeed a function, and
  • also a horizontal line test to make sure it is it one-to-one.

In other words,

The function will be one-to-one if it passes the vertical line test, and also if the horizontal line only cuts the graph of the function in one place.

The reason is that there must be only one x-value for each y-value.

Given the function

h\left(x\right)\:=\:x^3\:+\:7

Have a look at the attached graph.

  • The red portion represents the graph of the function h\left(x\right)\:=\:x^3\:+\:7.
  • The green portion represents the graph of x=2 which is basically a vertical line test. Vertical line indicates that it cuts the cuts the graph of the function in one place. So it is clear that h\left(x\right)\:=\:x^3\:+\:7 is indeed a function.
  • The blue line represents the graph of y=9, which is basically a horizontal line test. Horizontal line indicates that it cuts the cuts the graph of the function in one place. So it is clear that h\left(x\right)\:=\:x^3\:+\:7 is a one-to-one function, as there is only one x-value for each y-value.

Therefore, we conclude that the function is one-to-one.

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Calculate the straight line distance between the points (-10, -7) and (-8,1).<br> G.2(B)
tia_tia [17]

Answer:

2√(17) or about 8.2462 units.

Step-by-step explanation:

We want to determine the distance between the two points (-10, -7) and (-8, 1).

We can use the distance formula. Recall that:

\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Substitute and evaluate:

\displaystyle \begin{aligned} d &= \sqrt{((-10)-(-8))^2 + ((-7) - (1))^2} \\ \\ &=\sqrt{(-2)^2+(-8)^2} \\ \\ &= \sqrt{(4) + (64)} \\ \\ &= \sqrt{68}\\ \\ &= 2\sqrt{17}\end{aligned}

Hence, the distance between (-10, -7) and (-8, 1) is 2√(17) units or about 8.2462 units.

4 0
2 years ago
What’s the correct answer for this?
Mice21 [21]

。☆✼★ ━━━━━━━━━━━━━━  ☾  

First, you'd work out the centre value

It would be the opposite value to what is in the brackets

Thus, the centre value is (2, -4)

Plot this value on a graph

In order to find the radius, you must square root the 25

Thus, the radius would be 5

Plot some points with a radius of 5 from the centre and then draw the circle

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

。☆✼★ ━━━━━━━━━━━━━━  ☾

8 0
3 years ago
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