Final answer:
The correct statements about the function g(x) = -5x + 17 are that its range is all real numbers, its domain is all real numbers, and its graph is represented by y = -5x + 17.
Step-by-step explanation:
When analyzing the function g(x) = -5x + 17, we can evaluate the given statements as follows:
- A) The x-intercept of g occurs when g(x) = 0. Solving for x, we get 0 = -5x + 17, which simplifies to x = 17/5 or 3.4. Therefore, the x-intercept is 3.4, not 17. This statement is false.
- B) The range of g is all real numbers because it is a linear function with a non-zero slope, meaning it can take any value on the y-axis. This statement is true.
- C) The value for x is the input for g, not the output. This statement is false.
- D) The domain of g is all real numbers since there are no restrictions on the values that x can take for a linear function. This statement is true.
- E) The graph of g is indeed the graph of y = -5x + 17 because g(x) represents the y-value for any given x. This statement is true.
Therefore, the correct statements about the function g(x) are B) The range of g is all real numbers, D) The domain of g is all real numbers, and E) The graph of g is the graph of y = -5x + 17.