contestada

I’ll give BRAINLIEST if correct pls need ASAP

Part A: given the function
g(x) = |x+3| describe the graph of the function including the vertex domain and range

Part B: if the parent function
f(x) = |x| is transformed to
h(x) = |x| - 2 what Transformation occurs from
f(x) to h(x) how are the vertex and range of h(x) affected

Respuesta :

semsee45

Answer:

A)   The graph of function g(x) is V-shaped and has the following properties:

  • The vertex is (-3, 0)
  • The axis of symmetry is x = -3
  • The domain is the set of all real numbers: (-∞, ∞)
  • The range is [0, ∞)

B)  Translation of 2 units down.

Therefore:

  • The vertex is (0, -2)
  • The range is [-2, ∞)

Step-by-step explanation:

The absolute value parent function, f(x) = |x|, is defined as:

[tex]f(x)=\begin{cases}x \; &\text{if}\;x > 0\\0 \; &\text{if} \; x=0\\-x\; &\text{if}\;x < 0\end{cases}[/tex]

Therefore:

  • The slope of the line where x > 0 is positive.
  • The slope of the line where x < 0 is negative.

Its graph is V-shaped and has the following properties:

  • The x-intercept and y-intercept are at the origin (0, 0).
  • The vertex is at the origin (0, 0).
  • The axis of symmetry is x = 0 (y-axis).
  • The domain is the set of all real numbers: (-∞, ∞).
  • The range is the set of all real numbers greater than or equal to 0:  [0, ∞).

Part A

Given absolute value function:

[tex]g(x)=|x+3|[/tex]

The graph of function g(x) is the parent function f(x) translated 3 units to the left.

As the graph has only been translated horizontally, the domain and range are the same as the parent function.

Therefore, the graph of function g(x) has:

  • Vertex = (-3, 0)
  • Domain = (-∞, ∞)
  • Range = [0, ∞)

Part B

Given absolute value functions:

[tex]f(x)=|x|[/tex]

[tex]h(x)=|x|-2[/tex]

The graph of function h(x) is the parent function f(x) translated 2 units down.

As the graph has been translated vertically, the domain is the same as the parent function, but the vertex and range are different.

  • The y-value of the vertex of h(x) is 2 less than f(x).
    Therefore, the vertex is (0, -2).
  • The minimum value of range of h(x) is 2 less than f(x).
    Therefore, the range is [-2, ∞).