3. a function f is shown below. find the values of each: f(-2)= f(1)= f(5)= for which x - values is f(x)=2…
3. a function f is shown below. find the values of each: f(-2)= f(1)= f(5)= for which x - values is f(x)=2? 4. using the same graph as in problem 3, find each of the following items: a) the domain of the function, in interval notation. b) the range of the function, in interval notation. c) the values of the x - intercepts. d) the value of the y - intercept. e) the minimum value of the function. f) the maximum value of the function.
Answer
Explanation:
Step1: Determine domain
The domain is the set of all x - values for which the function is defined. Looking at the graph, the x - values range from - 3 to 6. So the domain is $[-3,6]$.
Step2: Determine range
The range is the set of all y - values that the function takes. From the graph, the lowest y - value is - 3 and the highest is 4. So the range is $[-3,4]$.
Step3: Find x - intercepts
The x - intercepts are the x - values where $y = f(x)=0$. From the graph, the x - intercepts are $x=-1,2,4$.
Step4: Find y - intercept
The y - intercept is the y - value when $x = 0$. From the graph, when $x = 0$, $y=-2$.
Step5: Find minimum value
The minimum value of the function is the lowest y - value on the graph. From the graph, the minimum value is $y=-3$.
Step6: Find maximum value
The maximum value of the function is the highest y - value on the graph. From the graph, the maximum value is $y = 4$.
Answer:
a) $[-3,6]$ b) $[-3,4]$ c) $x=-1,2,4$ d) $y=-2$ e) $y=-3$ f) $y = 4$