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

Tutors, please sign in to answer this question.

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.

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