In both cases you may well benefit from graphing the functions.
Do you recognize f(x) = (x + 1)^2 - 1 as a quadratic function, whose graph is that of a parabola that opens up? By comparing this to y = a(x-h)^2 + k, we see that a=1, h= -1 and k = -1. The vertex is at (h,k), which here is the point (-1, -1). This is the minimum value of the function. Thus, the range of this function is [-1, infinity).
Now for the function f(x) = 7x - 11: This is a linear function whose graph is (surprise!) a straight line. When x increases, y increases, without limits to either. Similarly, when x decreases, y decreases.
Thus the range includes all real numbers: (-infinity, infinity).
The answer is b) <span>4^2 + 7^2
proof
(3.-5) - (-1.2) = (4. -7), the length of vectAB(</span>(4. -7) =sqrt (<span>4^2 + 7^2)</span>
Answer:
A. 19,70,91
Step-by-step explanation:
Interior angle =180
19+70+91=180
A pair of lowercase letters represents a recessive gene.
For further clarification, if needed... If the punnett square was for dark hair being dominant over blonde hair, the offspring that was represented by two lowercase letters in a punnett square would have a phenotype of blonde hair.
Answer:
y = 4(x - 2)² + 48
Step-by-step explanation:
Given
y = 4x² - 16x + 64
Using the method of competing the square
Factor out 4 from 4x² - 16x
y = 4(x² - 4x) + 64
add/ subtract ( half the coefficient of the x- term)² to x² - 4x
y = 4(x² + 2(- 2)x + 4 - 4 ) + 64
= 4(x - 2)² - 16 + 64
= 4(x - 2)² + 48