Question

Enter a rule for each function f and g, and then compare their domains, ranges, slopes, and y-intercepts.The function f(x) has a slope of -2 and has a y-intercept of 3. The graph shows the function g(x).

Answer 1

The rule of the function f(x) is : -2x + 3

To find the rule of the function g(x) let's calculate the slope of the line

`m=(y2-y1)/(x2-x1)=(-11-5)/(4-0)=(-16)/(4)=-4`

The slope of the line is -4 and the intercept is 5 ( from the graph).

The rule of the function g(x) is : -4x + 5

The domains of f(x) and g(x) is All real numbers, because there is not any number of x which doesn't have a corresponding y-coordinate.

The ranges of f(x) and g(x) is All real numbers, because there is not any number of y which doesn't have a corresponding x-coordinate.

The slope of f(x) is greater than g(x) (-2 is greater than -4)

The y-intercept of f(x) is less than the y-intercept of g(x).(3 is less than 5)