Math

QuestionIdentify the linear function among these equations: f(x)=53xf(x)=5-\frac{3}{x}, f(x)=3x25f(x)=3x-\frac{2}{5}, f(x)=4x52xf(x)=4x-\frac{5}{2x}, f(x)=x4+3f(x)=|x-4+3|.

Studdy Solution

STEP 1

Assumptions1. A linear function is a function of the form f(x)=mx+bf(x) = mx + b, where mm and bb are constants. . The function f(x)f(x) is linear if and only if its graph is a straight line.
3. The function f(x)f(x) is linear if and only if it is of first degree, i.e., the highest power of xx in the function is1.

STEP 2

Examine the first equation f(x)=5xf(x)=5-\frac{}{x}.
This function is not linear because it is not of the form f(x)=mx+bf(x) = mx + b. The term x\frac{}{x} is not a constant or a multiple of xx.

STEP 3

Examine the second equation f(x)=3x25f(x)=3x-\frac{2}{5}.
This function is linear because it is of the form f(x)=mx+bf(x) = mx + b. Here, m=3m=3 and b=25b=-\frac{2}{5}.

STEP 4

Examine the third equation f(x)=4x2xf(x)=4x-\frac{}{2x}.
This function is not linear because it is not of the form f(x)=mx+bf(x) = mx + b. The term 2x\frac{}{2x} is not a constant or a multiple of xx.

STEP 5

Examine the fourth equation f(x)=x4+3f(x)=\mid x-4+3.
This function is not linear because the absolute value function x4+3\mid x-4+3 \mid is not of the form f(x)=mx+bf(x) = mx + b. The graph of an absolute value function is a V-shape, not a straight line.

STEP 6

After examining all the given equations, we find that the second equation f(x)=3x25f(x)=3x-\frac{2}{5} is the only one that represents a linear function.
So, the equation that represents a linear function is f(x)=3x25f(x)=3x-\frac{2}{5}.

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