F(x) = a(x - h)³ + k
The parent graph is F(x) = x³
k - shifts the parent graph up k-units (or down if it is negative). This is also called a vertical shift.
h - shifts the parent graph to the right h-units (or left if it is negative). This is also called a horizontal shift.
a - stretches the parent graph vertically by a factor of "a"
Additonally, the coordinate (h, k) is the center/vertex of the graph.
First, find the 40% discount.
40% of 195 is 78
195 x 0.40 = 78
Subtract that from 195
195 - 78 = 117
Now, find 66 2/3% of 117, since it is an additional reduction after the original discount.
2/3 = 0.667, so 66 2/3% is 66.667%
117 x 0.66667 = 78.00039
And subtract that from 117
117 - 78.00039 = 38.99961, which in dollars would be $38.99. (hundredths, etc. of a cent are usually just dropped; no rounding involved.)
The discount price would then be $38.99
The line g(x) has slope ...
(change in y)/(change in x) = (-18 -(-20))/(1 - 0) = 2
so can be written in slope-intercept form as
g(x) = 2x -20
The x-intercept of this line is at x=10.
0 = 2x -20 . . . . the x-intercept is where g(x) = 0
20 = 2x
10 = x
The circle also intersects the x-axis at x=10, so that will be one point that is shared by the circle and g(x). A graph shows there is also another point of intersection, (6, -8).
Yes, the linear function g(x) will intersect the circle at 2 points with positive x-coordinates.