<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis
(???, 0): 0 = - ln (x - 4)

0 = ln (x - 4)

1 = x - 4
<u> +4 </u> <u> +4 </u>
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)

1 = ln (x - 4)

e = x - 4
<u> +4 </u> <u> +4 </u>
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
<u> +4 </u> <u>+4 </u>
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
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transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
f(x) = - 3ˣ⁺⁵
= - 3⁰⁺⁵
= - 3⁵
= -243
Horizontal Asymptote: y = 0 <em>(explanation above)</em>
2x+3-5.32=68.82
2x= 71.14
x=35.57
each sneaker costs $35.57
Answer:
C
Step-by-step explanation:
|2x - 2| < 8
it implies that
2x - 2 < 8
2x -2 + 2 < 8 + 2
2x < 10
x < 5
or
-(2x - 2) < 8
-2x + 2 < 8
-2x + 2 - 2 < 8 - 2
- 2x < 6
x > -3 ( the sense of the inequality reverse because I divided by minus)
The solution can be combine to
-3<x<5
Side-Side-Side Theorem, Side-Angle-Side, Angle-Angle-Side, Angle-Side-Angle, and Hypotenuse-Leg for right triangles.
For example, for Side-Side-Side, if you prove all 3 sides of the triangle are congruent, then the triangle is congruent.