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)
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.