Answer:
Step-by-step explanation:
In this graph, we have the coordinate point (). Without translations, cos(0) = 0, which means that the graph is shifted to the right by
. We also know that the graph is shifted down by 1 because we have the point
(), but accounting for the right shift, this point should really by (
). cos(
) = -1, but on the graph it is -2, meaning that it is shifted down by 1.
Therefore, accounting for the right shift by and the shift down by 1, our equation is
.
Answer:
{y | y ≥ -11 }
Step-by-step explanation:
To answer a question like this, it is often helpful to graph the function or to rewrite it to vertex form.
f(x) = 3x^2 +6x -8
f(x) = 3(x^2 +2x) -8 . . . . factor the leading coefficient from x terms
f(x) = 3(x^2 +2x +1) -8 -3(1) . . . . complete the square*
f(x) = 3(x +1)^2 -11
The form of this equation tells you that the graph is a parabola that opens upward. Its vertex is (-1, -11), so the minimum value is -11. The range is the vertical extent of the function values, so goes upward from -11:
y ≥ -11
_____
* Vertex form is ...
f(x) = a(x -h)^2 +k
where "a" is the vertical scale factor and (h, k) is the vertex. When "a" is positive, the parabola opens upward; when it is negative, the parabola opens downward.
The square is completed by adding the square of half the x-coefficient inside parentheses, and subtracting the equivalent amount outside parentheses. Here, we had 2x inside parentheses, so we added (2/2)^2 = 1 inside and -3(1) outside, because "a" was 3.
_____
Brainly provides tools for properly rendering math symbols. 2-11 is not the same as ≥-11.
Answer:
Equation to represent the situation =
Step-by-step explanation:
Given:
Initial investment = Y
Growth rate (r) = 5% = 5 / 100 = 0.05
Number of year (n) = X year
Amount after X year = $800
Find:
Equation to represent the situation:
Computation:
Equation to represent the situation =