Given the graph note the graph is only defined on 34 httpsw

Given the graph (note, the graph is only defined on [-3,4] ) https://weber.instructure.com/courses/386771/files/67061083/preview

(a) Find x-intercepts

(b) Find y -intercept

(c) Find the interval(s) on which the function is increasing

(d) Find the interval(s) on which the function is decreasing

(e) Find local maximum (write your answer(s) as a point(s) with two coordinates, with comma and no space)

(f) Find local minimum (write your answer(s) as a point(s) with two coordinates, with comma and no space)

Solution

Answer:

(a) The x-intercept is the point where the graph intersects the x-axis. Since the x-axis is also the line y=0, the    y-value of this point will always be 0.

By looking at the graph, we can see that: the graph cuts the X - axis at x = -1 and at x = 2

Therefore, the X - intercept is ( -1 , 0 ) and ( 2, 0 ).

(b) The y-intercept is the point where the graph intersects the y-axis. Since the y-axis is also the line x=0,

the x-value of this point will always be 0.

By looking at the graph, we can see that: the graph cuts the Y- axis at y = -1

Therefore, the Y - intercept is ( 0 , -1 )

(c) A function f(x) is increasing if for x₁ < x₂ then f(x₁) f(x₂)

From the graph we can observe that the function is increasing in the interval ( 0 , 2 )

(d) A function f(x) is decreasing if for x₁ < x₂ then f(x₁) f(x₂)

From the graph we can observe that the function is increasing in the interval ( -3 , 0 ) U ( 2 , 4 )

(e) From the graph we can observe that the function has maximum 4 , at x = - 3

Hence the local maximum is ( - 3 , 4 )

(f) From the graph we can observe that the function has minimum - 2 , at x = 4

Hence the local minimum is ( 4, -2 )