Question

The table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=4x+3
Part A. Write a sentence to compare the slope of the two functions and shows the steps you used to determine the slope of f(x) and g(x)

Part B which functions has greater y-intercept. Justify

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Answer 1

Answer:

(a) g(x) has a greater slope

(b) g(x) has a greater y intercept

Step-by-step explanation:

Given

$x \to -1,0,1$

$f(x) \to -5,-1,3$

$g(x) = 4x + 3$

Solving (a): Compare the slopes

Slope (m) is calculated as:

$m =\frac{y_2 - y_1}{x_2 - x_1}$

So, for f(x), we have:

$m =\frac{-1- 0}{-5- -1}$

$m =\frac{-1}{-4}$

$m =\frac{1}{4}$

For g(x), we have:

Assume $g(x) = mx + c$ then the slope is m

Compare the above to $g(x) = 4x + 3$

Then the slope of g(x) is 4

g(x) has a greater slope

Solving (b): Function with greater y intercept

Here we set $x= 0$

From the table of f(x)

$f(x) = -1$ when $x = 0$

From $g(x) = 4x + 3$

$g(0) = 4 * 0 + 3$

$g(0) = 3$

Hence:

g(x) has a greater y intercept