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if f(x) is a linear function, which statement must be true ?
a) f(x) has no constant term
b) f(x) has no x^2 term
c) f(x) has no terms with a coefficient other than 1
d) f(x) has no x term​

Respuesta :

SaniShahbaz

Answer:

b) f(x) has no x^2 term

Step-by-step explanation:

The general form of a linear function is:

f(x) = ax + b

Where a and b are constant terms and x is the variable.

Option a:

This statement may or may not be true. We can have a linear function with no constant term for example f(x) = 5x is a linear function with no constant and f(x) = 5x + 5 is a linear function with a constant term. So option a cannot be the answer

Option b:

This statement is true for a linear function. x^2 term can be found in quadratic and higher degree polynomials. In linear function the power of variable must be 1.

Option c:

The function can have terms with coefficients other than 1 e.g f(x) = 5x + 5. So this is not true either

Option d:

f(x) must have x term. So this option is also not correct.

Therefore, the correct answer is option b.

Answer:

The correct statement is (b) which is f(x) has no [tex]x^2[/tex] term

Explanation:

The graph of a linear equation is a straight line. The general form of a linear equation is

ax + by + c = 0

Here, the coefficients a and b can't be zero simultaneously.

The term 'c' is a constant and can be zero.

We can see that the exponent on each variable x and y is 1. So, if the exponent in any variable is not 1 then that will not be a linear equation.

Other than this, the coefficients a and b can be zero at a time.

  • If a = 0 , then the x term will be zero.
  • If b = 0, then the y term will be zero.

Therefore, on the basis of these facts, we can conclude that the necessary condition for an equation is to be a linear equation is " it should not have any [tex]x^2[/tex] term"

If we have [tex]x^2[/tex] in our equation then it will be a quadratic equation.

Therefore, option b is correct.

Further Explanation:

Any function which is in the form ax+by+c=0 is called a linear function.

Linear function always represents a straight line.

The slope intercept form of a line is [tex]y=mx+b[/tex]. Here, m is the slope and b is the y-intercept.

The formula for slope of a straight is given by

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Learn more:

https://brainly.com/question/6108704 (Answered by  SociometricStar)

https://brainly.com/question/7876025 (Answered by Calculista)

Keywords:

  • Linear equation
  • Straight line
  • General form of linear equation
  • Slope intercept form of a line

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