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Which functions have a vertex with a x-value of 0? Select three options.
Of(x) = lxl
Of(x) = |x| +3
Of(x) = x + 31
Of(x)= |x|-6
Of(x)= x + 31-6

Which functions have a vertex with a xvalue of 0 Select three options Ofx lxl Ofx x 3 Ofx x 31 Ofx x6 Ofx x 316 class=


Answer :

Answer:

Options 1, 2, 4

Step-by-step explanation:

When you have a value inside the absolute value signs, that is moving the x value right or left. For example, f(x) = |x+3|, that is moving the x value left by 3.

When you have a value outside the absolute value signs, that is moving the y value up or down. For example, f(x) = |x| + 3, that is moving the y value up by 3.

Since you want to find the equations that have an x value of 0 for the vertex, you can move the y value all you want but cannot move the x value.

Options 1, 2, and 4, are the only ones that don't move the x values and has a vertex of 0.

semsee45

Answer:

f(x) = |x|

f(x) = |x| + 3

f(x) = |x| - 6

Step-by-step explanation:

The parent function for all the given functions is the modulus function f(x)=|x|.  

A modulus function gives the absolute value of a number or variable.  

The absolute value of a number is its positive numerical value.

Therefore, the range of f(x)=|x| is more than or equal to zero.

The graph of f(x)=|x| is:

  • Line y = x where x ≥ 0
  • Line y = -x where x ≤ 0
  • Vertex at (0, 0)

Translations

[tex]\textsf{For} \; a > 0:[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

For a modulus function to have a vertex with an x-value of zero after translation, the function can only be translated up or down.  If it was translated left or right, the x-value of the vertex would no longer be zero.

Therefore:

f(x) = |x|  →  No translation.  Vertex at (0, 0).

f(x) = |x| + 3  →  Translated 3 units up.  Vertex at (0, 3).

f(x) = |x + 3|  →  Translated 3 units left.  Vertex at (-3, 0).

f(x) = |x| - 6  →  Translated 6 units down.  Vertex at (0, -6).

f(x) = |x + 3| - 6  →  Translated 3 units left and 6 units down.  Vertex at (-3, -6).

So the functions that have a vertex with an x-value of zero are:

  • f(x) = |x|
  • f(x) = |x| + 3
  • f(x) = |x| - 6

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