Which of the following functions is graphed below?

Mathematics

1 answer:

kvv77 [185]2 years ago

4 0

Using translation concepts, it is found that the function graphed is defined by:

D. y = |x - 2| + 3.

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the function has the format of the absolute value function, y = |x|, which has vertex at (0,0). Here, the vertex is at (2,3), that is, the function was shifted:

2 units to the right, that is, x -> x + 2.

3 units up, that is, y -> y + 3.

Hence the definition is given by:

D. y = |x - 2| + 3.

More can be learned about translation concepts at brainly.com/question/4521517

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What is the constant term of the quotient when 2x^3-3x^2 + 4x-2 is divided by x^2-x+2?

AlladinOne [14]

Answer:

-1

Step-by-step explanation:

See the attachment for the polynomial long division. The constant in the quotient is -1.

_____

Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.

That could be a first guess in a "guess and check" solution approach.

<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).

<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2

Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.