Function rule is the relationship between input and output values. To find the function rule we have to observe the given data carefully that how input and output values are related to each other.
Answer:
1. y=5 and x=-5
2. y=2 and x=-4
Step-by-step explanation:
1.y=-5x-19
y=-6x-24
since both equations are equal to y, they are also equal to eachother
-5x-19=-6x-24
addition P.O.E.
x-19=-24
addition P.O.E.
x=-5
substitute x into one equation
y=-5*-5-19
y=6
2. y=-6x-22
y=-3x-10
since both equations are equal to y, they are also equal to eachother
-6x-22=-3x-10
addition P.O.E.
-22=3x-10
addition P.O.E.
-12=3x
division P.O.E.
-4=x
substitute x into one equation
y=-3*-4-10
y=2
Answer:
<h2>This equation has no natural roots.</h2>
Step-by-step explanation:
![3x^2+x-5=0\\\\\text{Use the quadratic formula for}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{For the given equation:}\\\\a=3,\ b=1,\ c=-5\\\\b^2-4ac=1^2-4(3)(-5)=1+60=61\\\\x=\dfrac{-1\pm\sqrt{61}}{(2)(3)}=\dfrac{-1\pm\sqrt{61}}{6}\notin\mathbb{N}](https://tex.z-dn.net/?f=3x%5E2%2Bx-5%3D0%5C%5C%5C%5C%5Ctext%7BUse%20the%20quadratic%20formula%20for%7D%5C%20ax%5E2%2Bbx%2Bc%3D0%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5C%5Ctext%7BFor%20the%20given%20equation%3A%7D%5C%5C%5C%5Ca%3D3%2C%5C%20b%3D1%2C%5C%20c%3D-5%5C%5C%5C%5Cb%5E2-4ac%3D1%5E2-4%283%29%28-5%29%3D1%2B60%3D61%5C%5C%5C%5Cx%3D%5Cdfrac%7B-1%5Cpm%5Csqrt%7B61%7D%7D%7B%282%29%283%29%7D%3D%5Cdfrac%7B-1%5Cpm%5Csqrt%7B61%7D%7D%7B6%7D%5Cnotin%5Cmathbb%7BN%7D)
Answer:
The range is { -1,3,7,11,15}
Step-by-step explanation:
The range is just the output values
f(-2) = 4(-2) +7 = -8+7 =-1
f(-1) = 4(-1) +7 = -4+7 = 3
f(0)= 4(0) +7 = 7
f(1) = 4(1) + 7 = 11
f(2) = 4(2) +7 = 8+7 = 15