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Temka [501]
2 years ago
15

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

Mathematics
1 answer:
Elza [17]2 years ago
6 0

Answer:

(a) The slope of f(x) is greater than the slope of g(x)

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

Step-by-step explanation:

Given

\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}

g(x) = 3x - 2

Solving (a): Compare the slopes

The slope (m) of f(x) is calculated as;

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

This gives:

m = \frac{f(0) - f(1)}{0 - 1}

m = \frac{f(0) - f(1)}{- 1}

Substitute values for f(0) and f(1)

m = \frac{-1 - 7}{- 1}

m = \frac{-8}{- 1}

m = 8

The slope of g(x) can be gotten using the following comparison

g(x) = mx + b

m \to slope

So:

g(x) = 3x -2

m = 3

m_{f(x)} > m_{g(x)}

Solving (b): Compare the y intercept

y intercept is when x = 0

From the table of f(x)

f(0) = -1

From the equation of g(x)

g(x) = 3x -2

g(0) = 3*0-2

g(0) =-2

<em></em>f(0) > g(0)<em></em>

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