Question

The table below (in the image) represents a linear function f(x) and the equation represents a function g(x):

PART A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).


PART B: Which function has a greater y-intercept? Justify your answer.

Please answer both questions <3<3<3

Answer 1

9514 1404 393

Answer:

A) The slope of f(x) is the amount of change in f(x) when x changes by 1. The slope of g(x) is the coefficient of x. The slope of f(x) is greater than the slope of g(x).

B) The y-intercept of f(x) is -1. The y-intercept of g(x) is -7. The y-intercept of f(x) is greater.

Explanation:

A) The slope of a function is the ratio of the change in function value to the change in input value. For f(x), we can use the convenient inputs 0 and 1 and look at the change in output (f(1) -f(0)) = (3 -(-1)) = 4. The slope of f(x) is 4.

When the function is given by a linear equation, the slope is the coefficient of x. For g(x), the coefficient of x is 2, so the slope of g(x) is 2.

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

__

B) The y-intercept is the function value for an input of 0. The table shows f(0) = -1. The equation shows g(0) = -7.

The y-intercept of f(x) (-1) is greater than the y-intercept of g(x) (-7).