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3 years ago

The absolute value function, f(x) = |x + 2|, is shown.

Mathematics

1 answer:

Georgia [21]3 years ago

5 0

ANSWER

all real numbers

EXPLANATION

The given absolute value function is

$f(x) = |x + 2|$

This function is obtained by shifting the graph of

$y = |x|$

to the left by 2 units.

Since the domain of the parent function is all real numbers, the domain of the transformed function is also all real numbers because the shifting the parent function horizontally or vertically does not affect the domain.

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Question 1

Galina-37 [17]

Answer:

Did you find the answer???

5 0

2 years ago

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

Mason spent 15.85for 3 notebooks and 2 boxes of markers. the boxes of markers cost 3.95 each, and sales tax was 1.23. Mason also

Likurg_2 [28]

Multiply the amount of the notebooks which is 3, by the cost of the notebook, which is $15.85. that is $47.55.

to find how much it costs with the coupon, do the notebook cost and subtract that by 0.75

$47.55 - 0.75 = $46.8

6 0

3 years ago

Read 2 more answers

How Many Solutions? 3x - 7 = 3(x - 3) + 2 No Solution One Solution Infinite Solution

prisoha [69]

Answer:

Infinite Solutions

Step-by-step explanation:

3x-7=3x(x-3)+2

3x-7=3x-9+2 - Distributive Property

3x-7=3x-7 - adding the right side together

3 0

3 years ago

HELP IS NEEDED FAST PLEASE

vfiekz [6]

Answer:

17.1

Step-by-step explanation:

If you have 15.50 and you divide 0.75 you get 20.6 and if you subtract 3.50 you get 17.1 which is your answer. Boom

7 0

2 years ago