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Ans(1):
Given equation is f(x)=-1.5x+6
we can plug any number like x=0 and x=2 to find the f(x) also called y-value
plug x=0
f(x)=-1.5x+6 =-1.5*0+6 =0+6 =6
Hence first point is (0,6)
plug x=2
f(x)=-1.5x+6 =-1.5*2+6 =-3+6 =3
Hence first point is (2,3)
now we can graph both points then join them to get final graph of f(x)=-1.5x+6
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Ans(2):
We can repeat exactly same process for f(x) = -1/2x-5.
So the final graph will look like attached picture:
PART 1
If I have graph f(x) then graph f(x + 1/3) would translate the graph 1/3 to the left.
For example, I have f(x) = x².Then
f(x + 1/3) = (x + 1/3)²
I draw the graph of f(x) = x² and the graph of f(x) = (x + 1/3)² on cartesian plane to know what's the difference between them.
PART 2
If I have graph f(x) then graph f(x) + 1/3 would translate the graph 1/3 upper.
For example, I have f(x) = x².Then
f(x) + 1/3 = x² + 1/3
I draw the graph of f(x) = x² and the graph of f(x) = x² + 1/3 on cartesian plane to know what's the difference between them.
SUMMARY
f(x+1/3) ⇒⇒ <span>f(x) is translated 1/3 units left.
f(x) + 1/3 </span>⇒⇒ <span>f(x) is translated 1/3 units up.</span>
If I have graph f(x) then graph f(x + 1/3) would translate the graph 1/3 to the left.
For example, I have f(x) = x².Then
f(x + 1/3) = (x + 1/3)²
I draw the graph of f(x) = x² and the graph of f(x) = (x + 1/3)² on cartesian plane to know what's the difference between them.
PART 2
If I have graph f(x) then graph f(x) + 1/3 would translate the graph 1/3 upper.
For example, I have f(x) = x².Then
f(x) + 1/3 = x² + 1/3
I draw the graph of f(x) = x² and the graph of f(x) = x² + 1/3 on cartesian plane to know what's the difference between them.
SUMMARY
f(x+1/3) ⇒⇒ <span>f(x) is translated 1/3 units left.
f(x) + 1/3 </span>⇒⇒ <span>f(x) is translated 1/3 units up.</span>