Answer:
A. The graph of
is the graph of
stretched vertically, flipped over the x axis, and shifted 7 units down.
Step-by-step explanation:
Given:
![F(x)=x^3\\G(x)=-2x^3-7](https://tex.z-dn.net/?f=F%28x%29%3Dx%5E3%5C%5CG%28x%29%3D-2x%5E3-7)
In order to transform
to
, we need to follow the following transformation rules:
1. Multiply the function by the number 2. According to transformation rules, multiplying a function by a positive number greater than 1 results in vertical stretch of the function's graph.
2. Multiply by -1. Multiplying a function by -1 flips it over the x axis.
3. Add -7 to the function obtained in step 2. When a negative number C is added to a function, then the graph shift down by C units. So, here the graph shifts down by 7 units.
Thus, the graph of
is the graph of
stretched vertically, flipped over the x axis, and shifted 7 units down.
Answer:
a=3w−y
Step-by-step explanation:
Step 1: Flip the equation.
−a+3w=y
Step 2: Add -3w to both sides.
−a+3w+−3w=y+−3w
−a=−3w+y
Step 3: Divide both sides by -1.
(-a)/1=-(3w+y)/1
a=3w−y
Answer:
see explanation
Step-by-step explanation:
Given
f(x) = x² - p(x + 1) - c
= x² - px - p - c ← in standard form
with a = 1, b = - p and c = - p - c
Given that α and β are the zeros of f(x), then
α + β = -
and αβ =
, thus
α + β = -
= p , and
αβ =
= - p - c
-----------------------------------------------------------
(α + 1)(β + 1) ← expand factors
= αβ +α + β + 1 ← substitute values from above
= - p - c + p + 1
= - c + 1 = 1 - c ← as required
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