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Can someone help me with 19-24... I need it to be worked out and answered... Please and thank you I really don't understand it, But it's due tomorrow morning so can someone please help... Thanks

Can someone help me with 19-24... I need it to be worked out and answered... Please-example-1
User Correcter
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Let me help you to understand this problem. Linear functions are those whose graph is a straight line. The form of a linear function is given by the following form:



y=f(x)=ax+b \\ \\ where \ a \ and \ b \ are \ constants \\ \\ \\ a:Represents \ the \ slope \ of \ the \ line \\ \\ b:Represents \ the \ y-intercept


The y-intercept occurs when x = 0.


So, our problem is to find the constants
a \ and \ b in each case. Therefore:


FIRST. (19)


f(0)=2, \ f(2)=4


The slope of a line can be found as follows:


a=(f(x_(2))-f(x_(1)))/(x_(2)-x_(1)) \\ \\ \\ f(x_(2))=f(2)=4 \\ \\ f(x_(1))=f(0)=2 \\ \\ \\ \therefore a=(4-2)/(2-0)=1


As the y-intercept occurs when x = 0, therefore:


b=f(0)=2


Accordingly, the first linear function is:


\boxed{y=f(x)=x+2}


SECOND. (20)


f(0)=7, \ f(3)=1


Applying the same reasoning as in the first exercise, the slope is:



f(x_(2))=f(3)=1 \\ \\ f(x_(1))=f(0)=7 \\ \\ \\ \therefore a=(1-7)/(3-0)=-2


And the y-intercept is:


b=f(0)=7


Accordingly, the second linear function is:


\boxed{y=f(x)=-2x+7}


THIRD. (21)


f(4)=-3, \ f(0)=-2


The slope is:



f(x_(2))=f(4)=-3 \\ \\ f(x_(1))=f(0)=-2 \\ \\ \\ \therefore a=(-3-(-2))/(4-0)=-(1)/(4)


And the y-intercept is:


b=f(0)=-2


Accordingly, the third linear function is:


\boxed{y=f(x)=-(1)/(4)x-2}


FOURTH. (22)


f(5)=-1, \ f(0)=-5


The slope is:



f(x_(2))=f(5)=-1 \\ \\ f(x_(1))=f(0)=-5 \\ \\ \\ \therefore a=(-1-(-5))/(5-0)=(4)/(5)


And the y-intercept is:


b=f(0)=-5


Accordingly, the fourth linear function is:


\boxed{y=f(x)=(4)/(5)x-5}


FIFTH. (23)


f(-2)=6, \ f(0)=-4


The slope is:



f(x_(2))=f(-2)=6 \\ \\ f(x_(1))=f(0)=-4 \\ \\ \\ \therefore a=(6-(-4))/(-2-0)=-5


And the y-intercept is:


b=f(0)=-4


Accordingly, the fifth linear function is:


\boxed{y=f(x)=-5x-4}


SIXTH. (24)


f(0)=3, \ f(-6)=3


The slope is:



f(x_(2))=f(-6)=3 \\ \\ f(x_(1))=f(0)=3 \\ \\ \\ \therefore a=(3-3)/(-6-0)=0


And the y-intercept is:


b=f(0)=3


Accordingly, the sixth linear function is:


\boxed{y=f(x)=3} \\ \\ This \ is \ a \ constant \ function

User Puffin GDI
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