Part 2: Match the function (column A) to its domain (column B). Write the letter of the domain beside the number.

Column A Column B
_____ 1. f(x)=(4x+5)/(x-2) A. D_f={x|x∈R \ ±3}
_____2. f(x)=(x^2-2x+1)/(x^2+2x+1) B. D_f={x|x∈R \ 2}
_____3. f(x)=(x + 2)/(x + 2) C. D_f={x|x∈R \ 1}
_____ 4. f(x)=(x-1)/(1-x) D. D_f={x|x∈R \ -2}
_____ 5. f(x)=3x/(x^2- 9) E. D_f={x|x∈R \ -1}
Part 3: Find the intercepts and zero of the following function.

Functions Intercepts Zeroes
f(x)=(1+x)/(3-x)
f(x)=(2x+1)/(x+4)

f(x)=(3x+6)/(x-2)

f(x)=(4x-2)/(x^2+4)

f(x)=(5x+16)/(x+4)


Part 4 : Given functions f(x)=-4x+9 , g(x)=2x-7, and h(x)=3x-1, Find;
A

____1. (f ⃘ g)(0)
____2. (g ⃘ g)(2)
____3. (g ⃘ f)(-1)
____4. (f ⃘ h)(4)
____5. (h ⃘ g)(-3)
B

-35
-40
13
20
37
55


Part 5: Determine whether the given is a rational function, a rational equation, rational inequality or none of these.

_____________1. y = 5x3 -2x + 1
_____________2. 8/x-8=x/(2x-1)
_____________3. 6x – 5 ≥ 0
X+3
_______________4. (x-1)/(x+1 )= x^2
_____________5. G(x) = 7x3 - 4√x + 1
X2 + , +3

Answer:Part 2: Domain Matching The domain of a function is the set of all possible input values (x-values) for which the function is defined. We need to find values of x that would make the denominator zero, as division by zero is undefined. 1. f(x) = (4x + 5) / (x - 2) - Denominator is zero when x = 2.- Domain: B. D_f = {x | x ∈ R \ 2}2. f(x) = (x² - 2x + 1) / (x² + 2x + 1) - Denominator is zero when x = -1.- Domain: E. D_f = {x | x ∈ R \ -1}3. f(x) = (x + 2) / (x + 2) - This function simplifies to f(x) = 1 (for x ≠ -2).- Domain: D. D_f = {x | x ∈ R \ -2}4. f(x) = (x - 1) / (1 - x) - Denominator is zero when x = 1.- Domain: C. D_f = {x | x ∈ R \ 1}5. f(x) = 3x / (x² - 9) - Denominator is zero when x = 3 or x = -3.- Domain: A. D_f = {x | x ∈ R \ ±3} Part 3: Intercepts and Zeroes - Intercepts:- x-intercept: Set y (or f(x)) = 0 and solve for x.- y-intercept: Set x = 0 and solve for y (or f(x)).- Zeroes: The zeroes of a function are the x-values where the function equals zero (same as the x-intercepts). Let's find the intercepts and zeroes for each function: 1. f(x) = (1 + x) / (3 - x) - x-intercept: (1 + x) / (3 - x) = 0 => x = -1- y-intercept: (1 + 0) / (3 - 0) = 1/3- Zeroes: x = -12. f(x) = (2x + 1) / (x + 4) - x-intercept: (2x + 1) / (x + 4) = 0 => x = -1/2- y-intercept: (2(0) + 1) / (0 + 4) = 1/4- Zeroes: x = -1/23. f(x) = (3x + 6) / (x - 2) - x-intercept: (3x + 6) / (x - 2) = 0 => x = -2- y-intercept: (3(0) + 6) / (0 - 2) = -3- Zeroes: x = -24. f(x) = (4x - 2) / (x² + 4) - x-intercept: (4x - 2) / (x² + 4) = 0 => x = 1/2- y-intercept: (4(0) - 2) / (0² + 4) = -1/2- Zeroes: x = 1/25. f(x) = (5x + 16) / (x + 4) - x-intercept: (5x + 16) / (x + 4) = 0 => x = -16/5- y-intercept: (5(0) + 16) / (0 + 4) = 4- Zeroes: x = -16/5PART 4:1. (f ⃘ g)(0) = f(g(0)) - First, find g(0): g(0) = 2(0) - 7 = -7- Then, find f(-7): f(-7) = -4(-7) + 9 = 37 Therefore, (f ⃘ g)(0) = 37 2. (g ⃘ g)(2) = g(g(2)) - First, find g(2): g(2) = 2(2) - 7 = -3- Then, find g(-3): g(-3) = 2(-3) - 7 = -13 Therefore, (g ⃘ g)(2) = -13 3. (g ⃘ f)(-1) = g(f(-1)) - First, find f(-1): f(-1) = -4(-1) + 9 = 13- Then, find g(13): g(13) = 2(13) - 7 = 19 Therefore, (g ⃘ f)(-1) = 19 4. (f ⃘ h)(4) = f(h(4)) - First, find h(4): h(4) = 3(4) - 1 = 11- Then, find f(11): f(11) = -4(11) + 9 = -35 Therefore, (f ⃘ h)(4) = -35 5. (h ⃘ g)(-3) = h(g(-3)) - First, find g(-3): g(-3) = 2(-3) - 7 = -13- Then, find h(-13): h(-13) = 3(-13) - 1 = -40 Therefore, (h ⃘ g)(-3) = -40 Matching the Answers: A B 1. (f ⃘ g)(0) 37 2. (g ⃘ g)(2) -13 3. (g ⃘ f)(-1) 19 4. (f ⃘ h)(4) -35 5. (h ⃘ g)(-3) -40PART 5:Let's classify each expression: 1. y = 5x³ - 2x + 1 - None of these. This is a polynomial function, not a rational function, equation, or inequality. 2. 8/(x - 8) = x/(2x - 1) - Rational equation. This is an equation where both sides are rational expressions (expressions with polynomials in the numerator and denominator). 3. 6x – 5 ≥ 0x + 3 - Rational inequality. This is an inequality involving a rational expression. 4. (x - 1) / (x + 1) = x² - Rational equation. This is an equation where both sides are rational expressions. 5. G(x) = 7x³ - 4√x + 1x² + x + 3 - None of these. This expression is not a rational function because it includes a square root term (√x). Summary: - Rational function: None- Rational equation: 2, 4- Rational inequality: 3- None of these: 1, 5

Answered by audreysagay20 | 2024-09-04