Mathematics, 26.06.2019 14:10 barn01

Which is the graph of g(x) = 2x – 1 + 3?

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Answer from: james22000

The graph in the attached figure

Step-by-step explanation:

we have

$g(x)=2^{x-1}+3$

This is a exponential function

The domain is the interval ----> (-∞,∞)

All real numbers

The range is the interval ----> (3,∞)

All real numbers greater than 3

The y-intercept of the function is the value of the function when the value of x is equal to zero

For x=0

$g(0)=2^{0-1}+3$

$g(0)=2^{-1}+3$

$g(0)=\frac{1}{2} +3$

g(0)=3.5

The y-intercept is the point (0,3.5)

using a graphing tool

The graph in the attached figure

Which is the graph of g(x) = 2x – 1 + 3?

Answer from: Quest

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.

Find the value of the variable and the length of each chord for #5 and #6.

Answer from: Quest

step-by-step explanation:

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