Ans(1):
Given equation is f(x)=-1.5x+6
we can plug any number like x=0 and x=2 to find the f(x) also called y-value
plug x=0
f(x)=-1.5x+6 =-1.5*0+6 =0+6 =6
Hence first point is (0,6)
plug x=2
f(x)=-1.5x+6 =-1.5*2+6 =-3+6 =3
Hence first point is (2,3)
now we can graph both points then join them to get final graph of f(x)=-1.5x+6
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Ans(2):
We can repeat exactly same process for f(x) = -1/2x-5.
So the final graph will look like attached picture:
Answer: the function g(x) has the smallest minimum y-value.
Explanation:
1) The function f(x) = 3x² + 12x + 16 is a parabola.
The vertex of the parabola is the minimum or maximum on the parabola.
If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.
The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.
When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).
Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.
Then, finding the minimum value of the function is done by finding the vertex.
I will change the form of the function to the vertex form by completing squares:
Given: 3x² + 12x + 16
Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4
That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).
Then the minimum value is 4 (when x = - 2).
2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>
The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.
When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2
Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.
If x=6 and y=3 is 9_______________________________________
A. It passes the vertical line test
Answer:
3 3/5 + 1 1/4 = <u>4 17/20</u>
7/8 + 1/12 =<u> 23/24</u>
8/9 - 2/5 = <u>22/45</u>
5 1/4 - 2 2/3 = <u>2 7/12</u>
Step-by-step explanation:
3 3/5 + 1 1/4
First convert into improper fractions
= 18/5 + 5/4
Now find the common denominator
72/20 + 25/20 =
97/20
Now simplify
4 17/20
<u>Next problem:</u>
7/8 + 1/12
find the common denominator
21/24 + 2/24 =
23/24
<u>Next problem:</u>
8/9 - 2/5
find the common denominator
40/45 - 18/45 =
22/45
<u>Next problem:</u>
5 1/4 - 2 2/3
First convert into improper fractions
21/4 - 8/3
find the common denominator
63/12 - 32/12 =
31/12
Now simplify
2 7/12
