Answer:
A
Step-by-step explanation:
The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.
This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.
An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.
Equation in slope-intercept form is y = 2x - 6
Step-by-step explanation:
- Step 1: Given slope of the line, m = 2. Form an equation y = mx + b
⇒ y = 2x + b ---- (1)
- Step 2: The line passes through the point (4,2). So it will satisfy the equation. Find b by substituting x = 4 and y = 2.
⇒ 2 = 2 × 4 + b = 8 + b
⇒ b = -6
- Step 3: Form the slope-intercept equation.
⇒ y = 2x - 6
5 - 5b < 1 - 4b
5 < 1 + b
4 < b
1 - 4b < 6 - 5b
1 + b < 6
b < 5
4 < b < 5
(The second less than sign is less than or equal to)
