Questions: Graph this function: y=4x-4+2

Transcript text: Graph this function: \[ y=4|x-4|+2 \]

Solution

Solution Steps

Step 1: Identify the function

The given function is: \[ y = 4|x - 4| + 2 \]

Step 2: Determine the vertex

The vertex of the function $y = 4|x - 4| + 2$ is at the point where the expression inside the absolute value is zero. Thus, set $x - 4 = 0$, which gives $x = 4$. Therefore, the vertex is at $(4, 2)$.

Step 3: Analyze the function

The function is a V-shaped graph due to the absolute value. The slope of the lines forming the V is 4 and -4, respectively, for $x > 4$ and $x < 4$.

Final Answer

The function $y = 4|x - 4| + 2$ is a V-shaped graph with a vertex at $(4, 2)$ and slopes of 4 and -4.

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 8, "ymin": 0, "ymax": 20}, "commands": ["y = 4*abs(x - 4) + 2"], "latex_expressions": ["$y = 4|x - 4| + 2$"]}

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >