Question

Graph each piecewise-defined function. f(x)={4−xif x\u003c21+2xif x≥2f(x) =
\begin{cases}
4 - x & 	ext{if } x \u003c 2 \
1 + 2x & 	ext{if } x \geq 2
\end{cases}

Accepted Answer

Identify the two pieces of the piecewise function: $$f(x) = x + 5$$ for $$x \leq 3$$ and $$f(x) = 14 - 3x$$ for $$x \u003e 3. $$Graph the first piece $$f(x) = x + 5$$ for all $$x$$ values less than or equal to 3. This is a line with slope 1 and y-intercept 5. Plot points such as $$(0, 5)$$ and $$(3, 8)$$ and draw the line up to $$x = 3. At$$ $$x = 3$$, mark the point on the first piece as a closed dot since the inequality includes $$x = 3. $$The point is $$(3, 8)$$ because $$3 + 5 = 8. $$Graph the second piece $$f(x) = 14 - 3x$$ for $$x \u003e 3. $$This is a line with slope $$-3$$ and y-intercept 14. Plot points such as $$(4, 2)$$ and $$(5, -1)$$ and draw the line starting just to the right of $$x = 3. At$$ $$x = 3$$, mark the point on the second piece as an open dot since the inequality is strict ($$x \u003e 3). $$Calculate $$f(3)$$ for the second piece to find the open dot location: $$14 - 3(3) = 5.$$

Graph each piecewise-defined function.
$f (x) = {\begin{matrix} 4 - x & if x < 2 \\ 1 + 2 x & if x \geq 2 \end{matrix}$

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Key Concepts

Piecewise-Defined Functions

Graphing Piecewise Functions

Domain and Interval Notation

Graph each piecewise-defined function. f(x)={4−xif x<21+2xif x≥2f(x) =\(\begin{cases}\)4 - x & \(\text{if }\) x < 2 \\1 + 2x & \(\text{if }\) x \(\geq\) 2\(\end{cases}\)