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.

1 answer

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.