Question

Which function is linear? A) f(x) = |7x| + 2 B) f(x) = 1 7x + 2 C) f(x) = 7x − 2 D) f(x) = |7x| − 2

Answer 1

Answer:

B) and C)

Step-by-step explanation:

The equation of alinear function in slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

A) f(x) = |7x| + 2  NO because we have absolute value of 7x

B) f(x)=17x + 2   YES, slope = 17 and y-intercept = 2

C) f(x) = 7x - 2   YES, slope = 7 and y-intercept = -2

D) f(x) = |7x| - 2   NO because we have absolute value of 7x

Answer 2

Linear function has highest power of variable is one. The option which represent the linear function are B and C.

$f(x) = 17x + 2$

$f(x) = 7x - 2$

What is linear function?

Linear function is the function in which the highest power of the unknown variable is one. Linear functions are used to model the real life problem in the mathematical expressions.

The linear function with dependent variable y and independent variable x can be written as,

$y=mx+c$

Here, $m$ is the slope of the function and $c$ is the y intercept.

Given information-

The option given in the problem has to check if they are linear function or not.

Let see all the options one by one as,

• A) The option A given is,

$f(x) = |7x| + 2$

Here, in the above function the mode of variable x is given. This mode represent the absolute value of the term 7x. Thus this does not represent the linear function.

• B)The option B given is,

$f(x) = 17x + 2$

The function match with the standard form of the linear function. Here, the slope is 17 and y intercept is 2.

Thus the option B shows the linear function.

• C)The option C given is,

$f(x) = 7x - 2$

This function match with the standard form of the linear function.

Here, the slope is 7 and y intercept is -2. Thus the option C shows the linear function.

• D)The option D given is,

f(x) = |7x| − 2

Here, in the above function the mode of variable x is given. This mode represent the absolute value of the term 7x. Thus this does not represent the linear function.

Thus the option which represent the linear function are B and C.

$f(x) = 17x + 2$

$f(x) = 7x - 2$

Learn more about the linear function here;

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