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3 years ago

Which graph shows a function and it’s inverse? HELP PLEASE

Mathematics

1 answer:

TEA [102]3 years ago

8 0

Answer:

Step-by-step explanation:

A function and its inverse are obtained by reflecting in the line y = x

Under a reflection in the line y = x

a point (x, y ) → (y, x )

In graph C

the red line has a point (0, 2 )

the blue line has a point (2, 0 )

Then graph C shows a function and its inverse

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Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

3 years ago

David bought a pizza for $12.74 and four medium drinks. Define a variable and write an expression to represent the total amount

SSSSS [86.1K]

You could say each drink is d. And we'll say the total is t. David got 4 drinks,

So... 12.74 + 4d = t

Hope this helps!

7 0

3 years ago

Multiply negative 1 over 2 multiplied by negative 1 over 2. Which of the following is correct?

krok68 [10]

Answer:

negative 1 over 4

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Which number line represents the solution set for the inequality ? HELP PLEASE

irga5000 [103]

Step-by-step explanation:

if you need any explanation you can ask

7 0

3 years ago

The product of five and a number plus 10 is at least thirty

inna [77]

Answer: Greater of equal sign

Step-by-step explanation:

5+10+x is greater than or equal to 30 ( use the greater of equal to sign)

7 0

3 years ago