Question

Function f(x): f(x) = (115 / (3x - 4)) if x > 1 f(x) = x if x > -1 a) Evaluate f(-1): [Answer: Enter your answer here] (1 point) b) Evaluate f(3): [Answer: Enter your answer here] (1 point) c) Describe the graph or insert a picture of your hand-drawn graph. If using a picture, please insert it using the 'image' function: [Answer: Enter your description or insert an image of the graph here] (2 points)

Answer 1

a) When x=−1, the function f(x) takes the value of −1 based on the given conditions.

b) When x=3, the function f(x) evaluates to 23 using the provided formula.

c) A detailed description of the graph is challenging in a text format. You can utilize graphing tools or draw the graph to visualize how the function behaves based on its defined conditions.

Step-by-step explanation:

a) Evaluate f(-1): For x ≤ -1, the function value is f(x) = x.

So, when x = -1, f(-1) = -1.

b) Evaluate f(3): For x > 1, the function value is f(x) = 115 / (3x - 4).

So, when x = 3, f(3) = 115 / (3(3) - 4) = 115 / 5 = 23.

c) Describe the graph:

The graph of the function f(x) consists of two parts. For x ≤ -1, it is a straight line with a slope of 1 and a y-intercept of 0.

For x > 1, it is a hyperbola with its vertical asymptote at x = 4/3 and its horizontal asymptote at y = 0.