In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = 12 to the number of x-
intercepts in the graph of g(t) = (t +32. Be sure to include the transformations that occurred between the parent function
f(t) and its image g(t)
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e
Chin

Both functions have one x-intercept each.

Step-by-step explanation:

The first function is

This is a parabola with vertices at the origin and has one x-intercept at t=0.

The transformed function is

The function g(t) is obtained by shifting the graph of f(t) to the left by 3 units.

This graph also has one x-intercept at x=-3.

Therefore both functions has the same number of x-intercepts

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.