The function g(x) is written in a confusing way.
The most logical form for g(x) according to the parent fucntion and the statements is this:
g(x) = [(-1/2)x]³
So, I will answer the question with such g(x).
And I will explain each step such that this answer is useful for you.
Statetements:
<span>a) The graph passes through the origin → True
The origin is the point (0,0)
Then plug in 0 into g(x).
The result is [ (-1/2) (0)] ³, which is 0.
So, indeed the point (0,0), the origin is in the graph.
b) As x approaches negative infinity, the graph of g(x) approaches infinity → TRUE
As x approaches negative infinity the denominator g(x) becomes greater and greater.
Try this: g(-10) g(-100), g(-1000).
g(-10) = 5³
g(-100) = (50)³
g(-1000) = (500)³
That shows you the trend: g(x) approaches infinity when x approaches to negative infinity.
c) As x approaches infinity, the graph of g(x) approaches infinity.→ False
As x approaches infinity, the graph of g(x) approaches negative infinity.
For example g(20000) = [- (20000/2) ]³ = - (10000)³
And as x grows g(x) becomes more negative.
d) The domain of the function is all real numbers → TRUE
The function g(x) accepst any value of x.
e) The range of the function is all real numbers → TRUE
g(x) goes from - infinity to + infinity and is continuous.
f) The graph of the function has three distinct zeros → FALSE
The only zero of g(x) is for x = 0.
</span>
When you divide two powers of the same base, you subtract the exponents:
![\dfrac{a^b}{a^c} = a^{b-c}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Ba%5Eb%7D%7Ba%5Ec%7D%20%3D%20a%5E%7Bb-c%7D%20)
This means that, in your case,
![\dfrac{7^n}{7^5} = 7^p \iff 7^{n-5} = 7^p \iff n-5 = p](https://tex.z-dn.net/?f=%20%5Cdfrac%7B7%5En%7D%7B7%5E5%7D%20%3D%207%5Ep%20%5Ciff%207%5E%7Bn-5%7D%20%3D%207%5Ep%20%5Ciff%20n-5%20%3D%20p%20)
So, if
, the equation becomes
![18-5 = p \iff p = 13](https://tex.z-dn.net/?f=%2018-5%20%3D%20p%20%5Ciff%20p%20%3D%2013%20)
Answer:
Step-by-step explanation:
When talking about reflection, we usually mean reflecting across a line, or axis. Reflecting a shape means looking at the mirror image on the other side of the axis. Consider the point (x,y), if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:
![(x,y)\rightarrow(-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%28-x%2Cy%29)
For triangle ABC we have:
![A(-4,2) \\ \\ B(-1,3) \\ \\ C(-1,-4)](https://tex.z-dn.net/?f=A%28-4%2C2%29%20%5C%5C%20%5C%5C%20B%28-1%2C3%29%20%5C%5C%20%5C%5C%20C%28-1%2C-4%29)
Therefore, the reflecting points are:
![A'(4,2) \\ \\ B(1,3) \\ \\ C(1,-4)](https://tex.z-dn.net/?f=A%27%284%2C2%29%20%5C%5C%20%5C%5C%20B%281%2C3%29%20%5C%5C%20%5C%5C%20C%281%2C-4%29)
Both the original triangle and the reflected one are shown below.
Answer:
Step-by-step explanation:
Wait ? I’m sorry I really don’t get it
The answer is 4
5(1/5) + (1/5)(15)
Multiply
5/1 • 1/5 = 1
1/5 • 15/1 = 3
Add
3 + 1 = 4