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. (1 point)

Answer 1

To determine if the graph is correct, we need to compare it with the given piecewise function.

From the piecewise function, we can identify three separate functions for different intervals of x:

For x < 1:
f(x) = 2x + 6

For 1 ≤ x < 6:
f(x) = -14x - 3

For x ≥ 6:
f(x) = 4x + 4

Let's analyze the graph:

- For x < 1, we see that the graph is a line with a positive slope intersecting the y-axis at 6. This matches with the function f(x) = 2x + 6.

- For 1 ≤ x < 6, we see that the graph is a line with a negative slope. However, it appears to intersect the y-axis at 3 instead of -3. So, it does not match the function f(x) = -14x - 3.

- For x ≥ 6, we see that the graph is a line with a positive slope intersecting the y-axis at 4. This matches with the function f(x) = 4x + 4.

Since the graph does not match the function f(x) = -14x - 3 for 1 ≤ x < 6, the answer is 2 for no.