Question

lesson 8.2) which statement about the graph of the rational function given is true? (1/2 point) f(x) = (3x - 7)/(x + 2) a. the graph has no asymptotes. b. the graph has no asymptotes. c. the graph has a vertical asymptote at x = -2. d. the graph has a horizontal asymptote at y = 3 (lesson 8.2) use the function to answer questions #5 - 7. (1/2 point each) f(x) = ((x - 1)(x + 2))/((x - 3)(x - 1)) 5. state the point of discontinuity, i.e., \hole,\ of the function. x = ______ 6. identify the x - intercept of the function. (_,_) 7. find the vertical asymptotes, if any, of the function. x = ______ learning goal from lesson 9.1 and 9.2 i can describe the similarities between the set of rational numbers and rational expressions. i can add, subtract, multiply, and divide rational expressions. how i did (circle one) i got it! im still learning it. (lesson 9.1) simplify the given expression. (1/2 point each) 8. (-x - 8)/(x²+9x + 8)

Explanation:

For question 4:

Step1: Recall asymptote rules

For a rational function $f(x)=\frac{ax + b}{cx + d}$, vertical asymptote is found by setting the denominator equal to 0. For $f(x)=\frac{3x - 7}{x + 2}$, set $x+2 = 0$.

Step2: Solve for vertical asymptote

$x+2=0$ gives $x=-2$. To find horizontal asymptote, since the degree of the numerator and denominator are the same (both degree 1), the horizontal asymptote is $y=\frac{a}{c}=\frac{3}{1} = 3$.

Step1: Simplify the function

For $f(x)=\frac{(x - 1)(x + 2)}{(x - 3)(x - 1)}$, cancel out the common factor $(x - 1)$ (for $x
eq1$). The function is undefined at $x = 1$.

Step1: Find x - intercept

Set $y = f(x)=0$. Since $f(x)=\frac{(x - 1)(x + 2)}{(x - 3)(x - 1)}$, after canceling $(x - 1)$ we consider $x+2=0$.

Step2: Solve for x

$x=-2$ is the x - intercept.

Answer:

C. The graph has a vertical asymptote at $x=-2$

For question 5: