
A linear function is a Function (mathematics) term of the form: : ''f''(''x'') = ''m'' ''x'' + ''c'' where ''m'' and ''c'' are constants. This function can also be written : ''y'' = ''m'' ''x'' + ''c'' and plotted on an ''x'',''y'' graph. It forms a straight line, as the name implies. The constant ''m'' is often called the slope or gradient while ''c'' is the y-intercept, which gives the point of intersection between the graph of the function and the ''y''-axis. Examples: *''f''(''x'')= 2''x'' + 1 ''(here m=2, c=1)'' *''f''(''x'') = ''x'' ''(m=1, c=0)'' *''f''(''x'')= 9 ''x'' - 2 *''f''(''x'')= -3 ''x'' + 4 On a line graph, changing ''m'' makes the line steeper or shallower, and changing ''c'' moves the line up or down. As mentioned, the line crosses the ''y''-axis at the co-ordinate (0,''c''). It crosses the ''x''-axis at (-''c'' / ''m'') (solving for 0 = ''m'' ''x'' + ''c'' we get ''x'' = -''c'' / ''m''). Polynomials
I found a different definition for a linear function in the French Wikipedia. It says that a linear function (fonction linéaire) is a function of the form f(x)=ax (necessarily passes through the zero). I made further research and I resume here my conclusion on the subject: A linear function is a function that respects both of the following conditions: It must be additive f(X1+X2)=f(X1)+f(X2) and it must be homogenous f(aX)= a f(x). the formula you give as a representation of a linear function: f(x)=mx+c is neither additive nor homogenous, hence it is not a linear function although it has a graphical representation of a line. Arie Finkelstein
See other meanings of words starting from letter:
Words begining with Linear_function:
Linear_function
Linear_function
Linear_functional
Linear_functionals
Linear_functions
Linear function
A linear function is a Function (mathematics) term of the form: : ''f''(''x'') = ''m'' ''x'' + ''c'' where ''m'' and ''c'' are constants. This function can also be written : ''y'' = ''m'' ''x'' + ''c'' and plotted on an ''x'',''y'' graph. It forms a straight line, as the name implies. The constant ''m'' is often called the slope or gradient while ''c'' is the y-intercept, which gives the point of intersection between the graph of the function and the ''y''-axis. Examples: *''f''(''x'')= 2''x'' + 1 ''(here m=2, c=1)'' *''f''(''x'') = ''x'' ''(m=1, c=0)'' *''f''(''x'')= 9 ''x'' - 2 *''f''(''x'')= -3 ''x'' + 4 On a line graph, changing ''m'' makes the line steeper or shallower, and changing ''c'' moves the line up or down. As mentioned, the line crosses the ''y''-axis at the co-ordinate (0,''c''). It crosses the ''x''-axis at (-''c'' / ''m'') (solving for 0 = ''m'' ''x'' + ''c'' we get ''x'' = -''c'' / ''m''). Polynomials
Linear function
I found a different definition for a linear function in the French Wikipedia. It says that a linear function (fonction linéaire) is a function of the form f(x)=ax (necessarily passes through the zero). I made further research and I resume here my conclusion on the subject: A linear function is a function that respects both of the following conditions: It must be additive f(X1+X2)=f(X1)+f(X2) and it must be homogenous f(aX)= a f(x). the formula you give as a representation of a linear function: f(x)=mx+c is neither additive nor homogenous, hence it is not a linear function although it has a graphical representation of a line. Arie Finkelstein
See other meanings of words starting from letter:
L
LA | LB | LC | LD | LE | LF | LG | LH | LI | LJ | LK | LM | LN | LO | LP | LR | LS | LT | LU | LW | LX | LY | LZ |Words begining with Linear_function:
Linear_function
Linear_function
Linear_functional
Linear_functionals
Linear_functions
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