Question

PLEASE HELP ME WITH THIS PROBLEMS 1.

Answer 1

Answers: -4, 5

Explanation:

`e^{x^(2)}=e^(x)*e^(20)`

`e^{x^(2)}=e^(x+20)`

x² = x + 20

x² - x - 20 = 0

(x + 4)(x - 5) = 0

x + 4 = 0 x - 5 = 0

x = -4 x = 5

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Answers:

• a. domain: (-∞,∞)
• b. range: (-∞, 0)
• c. y-intercept:
  `-(1)/(8)`
• d. horizontal asymptote: y = 0
• e. graph: see attachment

Step-by-step explanation:

domain: there are no restrictions on the x-value so x = All Real Numbers

range: since the new graph has a reflection then y < 0

y-intercept is when x = 0:

• y = -2⁰⁻³
• = -2⁻³
• =
  `-(1)/(2^(3))`
• =
  `-(1)/(8)`

horizontal asymptote: y ≠ 0 so the H.A. is y = 0

graph: The parent graph is: y = 2ˣ

The new graph of y = -2ˣ⁻³ has the following transformations:

1. reflection over the x-axis
2. horizontal shift 3 units to the right

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graph: see attachment

(0, 0) and (-1/3, 1)

(-1, ∞)

x = -1