Ask a New Question
Menu

Function 1 is defined by the equation y = 4x - 5, and the function 2 is represented by the graph below.

A coordinate plane is shown. 

The x-axis ranges from -9 to 9, and the y-axis ranges from -9 to 9. 

A straight, diagonal line is drawn, extending from the upper left quadrant to the lower right quadrant of the graph. The line passes through the point (0, 1), and slopes downwards and to the right.

Which statement about the function is true?
Responses
A Function 2 has the greater rate of change, and function 1 has the greater y-intercept.Function 2 has the greater rate of change, and function 1 has the greater y -intercept.
B Function 2 has the greater rate of change and the greater y-intercept.Function 2 has the greater rate of change and the greater y -intercept.
C Function 1 has the greater rate of change and the greater y-intercept.Function 1 has the greater rate of change and the greater y -intercept.
D Function 1 has the greater rate of change, and function 2 has the greater y-intercept.

1 answer

To determine which statement about the functions is true, let's analyze both functions based on their equations and characteristics.

Function 1:

  • The equation is given as \( y = 4x - 5 \).
  • The slope (rate of change) is 4, meaning for every unit increase in \( x \), \( y \) increases by 4.
  • The y-intercept (the value of \( y \) when \( x = 0 \)) is at \( -5 \) (the point (0, -5)).

Function 2:

  • The information suggests that Function 2 is a diagonal line that passes through the point (0, 1) and slopes down to the right.
  • Since it slopes downwards, it has a negative slope.
  • The y-intercept is 1 (the point (0, 1)).

Now, let's compare the two functions based on rate of change (slope) and y-intercept:

  1. Rate of Change:

    • Function 1 has a slope of 4.
    • Function 2 has a negative slope (exact value is not specified, but it is certainly less than 0).
    • Therefore, Function 1 has the greater rate of change.

  2. Y-Intercept:

    • Function 1 has a y-intercept of -5.
    • Function 2 has a y-intercept of 1.
    • Therefore, Function 2 has the greater y-intercept.

Based on this analysis:

  • Function 1 has the greater rate of change.
  • Function 2 has the greater y-intercept.

The correct answer is: D. Function 1 has the greater rate of change, and function 2 has the greater y-intercept.