the function f is defined as follows. f(x)={ -3x + 4 if x < 1; 2x - 1 if x >= 1} (a) find the domain of the…
the function f is defined as follows. f(x)={ -3x + 4 if x < 1; 2x - 1 if x >= 1} (a) find the domain of the function. (b) locate any intercepts. (c) graph the function. (d) based on the graph, find the range. (a) the domain of the function f is (-∞,∞). (type your answer in interval notation.) (b) locate any intercepts. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. the intercept(s) is/are. (type an ordered pair. use a comma to separate answers as needed.) b. there are no intercepts.
Answer
Explanation:
Step1: Find x - intercepts
For $x < 1$, set $y=-3x + 4=0$. Then $3x = 4$, so $x=\frac{4}{3}$. But $\frac{4}{3}\nless1$, so this is not a valid x - intercept for this part of the piece - wise function. For $x\geq1$, set $y = 2x-1=0$. Then $2x=1$, so $x=\frac{1}{2}$. But $\frac{1}{2}\ngeq1$, so this is not a valid x - intercept for this part of the piece - wise function. For y - intercept, set $x = 0$. Since $0<1$, $y=-3(0)+4=4$. The y - intercept is the point $(0,4)$.
Step2: Conclusion on intercepts
The intercept is the point $(0,4)$.
Answer:
A. The intercept(s) is/are $(0,4)$