Answer:
c) 3 units
d) g(x) - f(x) = x² + 2x
e) (-∞, -2] ∪ [0, ∞)
Step-by-step explanation:
<h3><u>Part (c)</u></h3>
To calculate the length of FC, first find the coordinates of point C.
The y-value of point C is zero since this is where the function f(x) intercepts the x-axis. Therefore, set f(x) to zero and solve for x:
As point C has a <u>positive</u> x-value, C = (1, 0).
To find point F, substitute the x-value of point C into g(x):
⇒ F = (1, 3).
Length FC is the <u>difference</u> in the y-value of points C and F:
<h3><u>Part (d)</u></h3>
Given functions:
Therefore:
<h3><u>Part (e)</u></h3>
The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):
Point A is the <u>y-intercept</u> of both functions, therefore the x-value of point A is 0.
To find the x-value of point E, equate the two functions and solve for x:
As the x-value of point E is negative ⇒ x = -2.
Therefore, the values of x for which g(x) ≥ f(x) are:
- <u>Solution</u>: x ≤ -2 or x ≥ 0
- <u>Interval notation</u>: (-∞, -2] ∪ [0, ∞)
This is not possible. A triangle is either acute (all angles less than 90 degrees), right (one 90 degree angle), or obtuse (an angle with more than 90 degrees). There can not be an "acute right triangle."
Are correct...all of the above