Compare the functions shown below: f(x)

polynomial graph with x intercepts at negative 3, negative 2, 1, 2, y intercept at negative 12
g(x)

trig graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3
Over the interval x = 0 to x = 2π h(x) = 2x3 − 2x2 − 3x + 2

Which function has the most x-intercepts?
f(x)
g(x)
h(x)
All three functions have the same number of x-intercepts.

Question 2(Multiple Choice Worth 2 points)
(09.05)

Compare the functions shown below:

f(x) = 3 cos 2x + 4
g(x)

cosine graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3
h(x)

x y
−6 −11
−5 −6
−4 −3
−3 −2
−2 −3
−1 −6
0 −11

Which function has the greatest maximum y-value?
f(x)
g(x)
h(x)
All three functions have the same maximum y-value.

no this is a nonlinear negative

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

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step-by-step explanation: