Question

Is this the correct graph for the piecewise function f(x)=⎧⎩⎨⎪⎪2x+6 if x<1−14x−3 if 1≤x<64+4x if x≥6
?

Enter 1 for yes or 2 for no.

Answer 1

I'm unable to see the graph, but I can help you determine if a piecewise function is graphed correctly if you describe it or provide details about features in the graph.

From the function you provided:

\[
f(x) =
\begin{cases}
2x + 6 & \text{if } x < 1 \\
-14x - 3 & \text{if } 1 \leq x < 6 \\
4 + 4x & \text{if } x \geq 6
\end{cases}
\]

1. For \( x < 1 \): The function is a line with a slope of 2 and y-intercept of 6 when extended to the left up to 1 (not inclusive).
2. For \( 1 \leq x < 6 \): The function is a line with a slope of -14 and y-intercept of -3 that starts at (1, -14(1)-3) and ends just before (6, ...).
3. For \( x \geq 6 \): The function is a line with a slope of 4 that starts at (6, 4 + 4(6)).

Check if these characteristics correctly appear in the graph you have. If they do, enter 1; otherwise, enter 2.