Problem 63 college algebra Please show all work Determine wh

Problem 63 (college algebra). Please show all work.

Determine whether the equation is a function. y = 2x^2 - 9x -5 Yes No

Solution

if the same x can give you two different y values, it is not a function.

Some things to look for that make it not a function:
| y |, y^2, +/- x

in a function, x can not be repeated
so you can\'t have both (1,2) and (1,-3) in a function
you can\'t have both (4,2) and (4,-2) in a function (which would come from x = y^2, or y = +/- sqrt(x)

you CAN have (4,16) and (-4, 16) (two different x-values giving the same y-value)

EDIT: careful, Jaya... a function can be a function without being 1-1 (not repeating either x or y values)
y-values can be repeated in a function, but x-values cannot

in otherwords: your letter grade is a function of your numerical score (if you get a 94 in math, that will be an A)

but your numerical score is not a function of the letter grade (if you get an A in math, you don\'t know your average for sure-- it could be a 93 or 94 or 95 or 94.5 or.....)

y = sqrt(x) is a function
sqrt(25) = 5 (and only 5, the principal root)

this is different than solving y^2 = x
then if x = 25, you could be either 5 or -5

Now for this equation, let\'s use the following values for x: (-2, -1, 0, 1, 2)
y1 = 2(-2)² - 9(-2) - 5 = 21
y2 = 2(-1)² - 9(-1) - 5 = 6
y3 = (2*0) - 9(0) - 5 = -5
y4 = 2(1)² - 9(1) - 5 = -12
y5 = 2(2)² - 9(2) - 5 = -15

This is indeed a function.

Hope this helps