Questions: Graph the function. Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima. f(x) = 3 - x Use the graphing tool to graph the equation. Determine on which interval(s) f(x) is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function f is increasing on the interval . (Type your answer in interval notation. Use a comma to separate answers as needed.) B. There is no interval on which the function f(x) is increasing.

Graph the function. Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima.

f(x) = 3 - x

Use the graphing tool to graph the equation. Determine on which interval(s) f(x) is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The function f is increasing on the interval .
(Type your answer in interval notation. Use a comma to separate answers as needed.)
B. There is no interval on which the function f(x) is increasing.

Transcript text: Graph the function. Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima. \[ f(x)=3-|x| \] Use the graphing tool to graph the equation. Determine on which interval(s) $f(x)$ is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function $f$ is increasing on the interval $\square$ . (Type your answer in interval notation. Use a comma to separate answers as needed.) B. There is no interval on which the function $f(x)$ is increasing.

Solution

Solution Steps

Step 1: Define the function

The function given is $ f(x) = 3 - |x| $.

Step 2: Determine the intervals of increase and decrease

The function $ f(x) = 3 - |x| $ is a V-shaped graph with a vertex at $ x = 0 $. It increases on the interval $ (-\infty, 0] $ and decreases on the interval $ [0, \infty) $.

Step 3: Identify the relative maxima and minima

The function has a relative maximum at $ x = 0 $ with $ f(0) = 3 $. There are no relative minima.

Final Answer

The function $ f(x) = 3 - |x| $ is increasing on the interval $ (-\infty, 0] $.

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -2, "ymax": 4}, "commands": ["y = 3 - abs(x)"], "latex_expressions": ["$y = 3 - |x|$"]}

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