then explain in words or show work.
a) f(x) = 4x^{2} - 7x +3
b) g(x) = 10 over x+7
c) f(x) = √4x - 16
d) g(x) = 2x over x-3
e) f(x) = 3x -9
then explain in words or show work.
a) f(x) = 4x^{2} - 7x +3
b) g(x) = 10 over x+7
c) f(x) = √4x - 16
d) g(x) = 2x over x-3
e) f(x) = 3x -9
Hello Char,
The domain is all the x-values, and the range is all the y-values.
a) f(x) = 4x^{2} - 7x +3
This is a polynomial. There are no denominators (so no division-by-zero) and no radicals (so no square-root-of-a-negative). There are no values that you can't plug in for x. When you have a polynomial, the answer is always the domain is "all x" or all real. Answer written in interval notation will be (-∞, +∞).
b) g(x) = 10 over x+7
The domain is all the values that x is allowed to take on. The only issue with this function is that you need to be careful not to divide by zero. So the only values that x can not take on are those which would cause division by zero. So ,set the denominator equal to zero and solve; your domain will be everything else.
set x + 7 = 0
-7 -7
----------------------------
x = -7
The domain is "all x not equal to -7". Answer in interval notation will be (-∞, -7) U (-7, +∞)
c) f(x) = √4x - 16
The domain is all values that x can take on. The only issue with this function is that you cannot have a negative inside the square root. So , set the insides of radical sign greater-than-or-equal-to zero, and solve. The result will be the domain.
4x - 16 ≥ 0 (add 16 on both sides)
16 16
--------------------
4x ≥ 16
(4x/4) ≥ 16/4 (divide by 4 on both sides)
x ≥ 4
The domain is " all x ≥ 4". Answer in interval notation will be
[4, +∞).
Problems d and e are same as b and a respectively.
I hope this helps you. If you've any questions you can ask me or any other tutor will be glad to help you.