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Given f(x) = -3x - 2, find the following:

a) f(0)
b) x-intercept of f(x)
c) y-intercept of f(x)
d) Vertex of the graph of f(x)

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Final answer:

To find the required values for f(x) = -3x - 2, f(0) is -2 (y-intercept), the x-intercept is at (2/3, 0), the y-intercept is at (0, -2), and the function does not have a vertex as it is linear.

Step-by-step explanation:

The student's question involves finding specific values for the linear function f(x) = -3x - 2. Here is how we find each of the requested points:

  • a) f(0): To find f(0), simply substitute x with 0 in the function. The result is f(0) = -3(0) - 2, therefore f(0) = -2. This is the y-intercept of the function.
  • b) x-intercept: To find the x-intercept, set the function equal to zero and solve for x: 0 = -3x - 2. Thus, x = -2 / -3, giving us the x-intercept at (2/3, 0).
  • c) y-intercept: The y-intercept is the value of f(x) when x=0, which we already found to be -2. This corresponds to the point (0, -2) on the graph.
  • d) Vertex of the graph: Since f(x) is a linear function, it does not have a vertex which is typically defined for quadratic functions. Instead, the graph is a straight line, and every point on the line is as crucial as any other.
User Carl Parker
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