Question

HELP with these questions

Answer 1

Step-by-step explanation:

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)

            $\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

            0 = ln (x - 4)

            $e^{0} = e^{ln (x - 4)}$

             1 = x - 4

          +4      +4

             5 = x

(5, 0)

(???, 1): 1 = - ln (x - 4)

            $\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

            1 = ln (x - 4)

            $e^{1} = e^{ln (x - 4)}$

             e = x - 4

          +4      +4

         e + 4 = x

          6.72 = x

(6.72, 1)

Domain: x - 4 > 0

                 +4  +4  

               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  (explanation above)