Question

I need help on question 1 of symbolic representation

Answer 1

Explanation:

Symbolic representation here means defining the function using variables such as x and y (or f(x)).

An example would be f(x) = 4x+3.

Here, we are given two points on the linear function (which is a line), namely

f(4)=5, which implies P1(4,5) is a point P1 on the line, and

f(-7)=5, which implies P2(-7,5) is another point P2 on the line.

With the usual notation that

P1 has the coordinates (x1,y1)

P2 has the coordinates (x2,y2),

we see that

x1=4, y1=5

x2=-7, y2=5

which can be used in the standard equation for a line given two points P1 and P2:

m = slope = (y2-y1)/(x2-x1) = (5-5)/(-7-(4)) = 0/11 = 0

equation of the line

y = m(x-x1) + y1, which simplifies to

y = 0(x-4) + 5, which further simplifies to

y=5 (which is a horizontal line).

Answer 2

f(x) = 0x + 5

Explanation:

Lets use the slope formula to determine the slope of this graph:

`m=(y_(2)-y_(1)  )/(x_(2)-x_(1) ) \\\\m=(5-5 )/(4-(-7)) \\\\m=0`

SO we know the slope is zero.

If we know the slope is zero, then the y intercept must be at 5.

So the equation would be:

f(x) = 0x + 5