Question

Look at the graphs and their equations below. Then fill in the information about the coefficients A, B, C, and D.

Answer 1

The coefficients are classified as follows

Positive coefficients: A and B

Negative coefficients: C and D

Coefficient closest to zero: C

Coefficient of greatest value: B

Effects of coefficients of absolute value function graph

The coefficients in an absolute value function have specific effects on the graph, influencing its shape, orientation, and position.

When positive the graph opens upward, forming a "V" shape.

The larger the coefficient, the narrower the opening of the graph.

When negative the graph opens downward, forming an inverted "V" shape.

The smaller the coefficient, the wider the opening of the graph.

Answer 2

Given:

Aim:

We need to find the coordinates and The sign of the equation.

Step-by-step explanation:

`We\text{ know that y=a\mid x\mid is upside and y}\ge\text{0 when a >0 and downside and y}\leq\text{owhen a<0}`

The coefficient of the given functions are

`y=A|x|\text{ is positive}`

`y=B|x|\text{ is positive}`

`y=C|x|\text{ is negative}`

`y=D|x|\text{ is negative}`

The coefficient is closest to zero.

Comparing the graph of y=A|x| and y=B|x|, we get y=A|x| is wider than y=B|x|.

[tex]A

Comparing the graph of y=C|x| and y=D|x|, we get y=D|x| is wider than y=C|x|.

[tex]C

Comparing the graph of y=A|x| and y=C|x|, we get y=C|x| is wider than y=A|x|.

[tex]C The coefficient is closest to zero y=C|x|.

The coefficient with the greatest value.

Comparing the graph of y=B|x| and y=D|x|, we get y=D|x| is wider than y=B|x|.

[tex]D The coefficient with the greatest value is y=B|x|. .