move at least one of the 9 guide points below to complete the graph of $y = |x + 4| - 1$. moving the red…

move at least one of the 9 guide points below to complete the graph of $y = |x + 4| - 1$. moving the red points changes the vertical stretch or compression. moving the blue point shifts the function left/right/up/down. click the buttons below to start over or reflect over the x-axis.\nreset reflect over x-axis

move at least one of the 9 guide points below to complete the graph of $y = |x + 4| - 1$. moving the red points changes the vertical stretch or compression. moving the blue point shifts the function left/right/up/down. click the buttons below to start over or reflect over the x-axis.\nreset reflect over x-axis

Answer

Explanation:

Step1: Identify vertex of target function

The vertex form of an absolute value function is $y = |x - h| + k$, where $(h,k)$ is the vertex. For $y = |x + 4| - 1$, rewrite as $y = |x - (-4)| + (-1)$, so vertex is $(-4, -1)$.

Step2: Shift the blue vertex point

Move the original blue vertex point $(0,0)$ left 4 units and down 1 unit to $(-4, -1)$.

Step3: Adjust red points (vertical shift)

For each red point on the original graph $y=|x|$, apply the same horizontal shift left 4 and vertical shift down 1:

  • Original $(1,1)$ → $(1-4, 1-1)=(-3, 0)$
  • Original $(2,2)$ → $(2-4, 2-1)=(-2, 1)$
  • Original $(3,3)$ → $(3-4, 3-1)=(-1, 2)$
  • Original $(4,4)$ → $(4-4, 4-1)=(0, 3)$
  • Original $(5,5)$ → $(5-4, 5-1)=(1, 4)$
  • Original $(-1,1)$ → $(-1-4, 1-1)=(-5, 0)$
  • Original $(-2,2)$ → $(-2-4, 2-1)=(-6, 1)$
  • Original $(-3,3)$ → $(-3-4, 3-1)=(-7, 2)$
  • Original $(-4,4)$ → $(-4-4, 4-1)=(-8, 3)$

Answer:

  1. Move the blue vertex point to $(-4, -1)$.
  2. Move each red point to the corresponding shifted coordinates: $(-3, 0)$, $(-2, 1)$, $(-1, 2)$, $(0, 3)$, $(1, 4)$, $(-5, 0)$, $(-6, 1)$, $(-7, 2)$, $(-8, 3)$ to form the graph of $y = |x + 4| - 1$.