9.2k views
1 vote
The table below represents a quadratic function. Identify the interval of decrease. 0 1 0 1 X Y X -4 -3 -2 -1 16 9 4 1 type your answer... 2 3 4 49 16​

The table below represents a quadratic function. Identify the interval of decrease-example-1

1 Answer

5 votes

The quadratic function's table shows a decrease from X = 4 to X = 1. The graph of "g(x)" is a translation of "|x|," accurately represented by "g(x) = |x - 1| - 1." The statements about range and domain are correct.

1. For the quadratic function represented by the table, the interval of decrease can be identified by examining the values of Y corresponding to different X-values. From the given data, the interval of decrease occurs from X = 4 to X = 1, where the Y-values decrease from 16 to 1.

2. The graph of function g(x) is a transformation of the parent function f(x) = |x|, translated 1 unit right and 1 unit down. The peak of the broad V-shape is located at (1, -1), and it intersects the x-axis at (-1, 0) and (3, 0).

The translation is accurately described by the equation g(x) = |x - 1| - 1, indicating a shift of 1 unit to the right and 1 unit down from the parent function.

Regarding the statements:

- The range is correctly described as "y ≤ 1," considering the downward shift of 1 unit.

- The domain is accurately stated as "all real numbers."

- The given equation "g(x) = |x + 1| - 1" represents a translation of the parent function, but it's not consistent with the described transformation.

In summary, the graph of "g(x)" is a translation of "f(x) = |x|" with the correct equation "g(x) = |x - 1| - 1," and the statements about range and domain are accurate.

The question probable may be:

1. Consider the quadratic function represented by the table. Identify the interval of decrease. The values of X and Y are given as follows:

X: -4, -3, -2, -1, 0, 1, 2, 3, 4

Y: 16, 9, 4, 1, 0, 1, 4, 9, 16

2. The graph of function g(x) is shown below. select all the true statements.

The graph is like a broad v shape whose peak is it coordinate ( 1 , -1) and then passes hru x axis at ( -1 , 0) and( 3 , 0)

was translated 1 unit right and 1 unit down from its parent function f(x) = |x|

can be represented by the equation g(x) = |x - 1| - 1

range y ≤ 1

domain: all real numbers

can be represented by the equation g(x) = | x+1 | - 1

User Tsap
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories