Question

Use the four functions below for this question: f(x) x f(x) −1 -7 1 1 2 5 g(x) (graph) a line going through the point, negative 2, 5, and 0, negative 3 h(x) h(x) = −4x + 3 j(x) Cameron adds 4 new hats to his collection each year. He started with only 3. QUESTION BELOW Compare and contrast these four functions using complete sentences. Focus on the slope and y-intercept first, and then on any additional properties of each function

Answer 1

The slope of f(x) is 4 and y-intercept is -3. It is an decreasing function.

The slope of g(x) is -4 and y-intercept is -3. It is an decreasing function.

The slope of h(x) is -4 and y-intercept is 3. It is an increasing function.

The slope of j(x) is 4 and y-intercept is 3. It is an increasing function.

Explanation:

The slope intercept form of a line is

`y=mx+b`

Where, m is slope and b is y-intercept.

If a line passing though two points, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

From the given information it is noticed that the function f(x) passing through the points (1,1) and (2,5).

`y-1=(5-1)/(2-1)(x-1)`

`y=4x-4+1`

`f(x)=4x-3`

The slope of f(x) is 4 and y-intercept is -3. It is an decreasing function.

From the given information it is noticed that the function g(x) passing through the points (0,-3) and (-2,5).

`y+3=(5+3)/(-2-0)(x-0)`

`g(x)=-4x-3`

The slope of g(x) is -4 and y-intercept is -3. It is an decreasing function.

The function h(x) is

`h(x)=-4x+3`

The slope of h(x) is -4 and y-intercept is 3. It is an increasing function.

It is given the initial amount of hat is 3 and number of hats increased by 4. So the function j(x).

`f(x)=4x+3`

The slope of j(x) is 4 and y-intercept is 3. It is an increasing function.