mathematical, graph sketching?

Question

1)consider the formula y=x^2+2x-3 sketch the graph of the function. 2) consider the formula y=3e^x sketch the graph of the function. can anybody show me exactly how to solve these problems? explaining it in simple terms. cheers

Answer 1

Question 1
f(x) = x² + 2x - 3
f `(x) = 2x + 2 = 0 for turning point
2x = - 2 gives x = -1 for turning point
Turning point is (-1,- 4)
f "(x) = 2 which is +ve which means that the turning point is a Minimum turning point

f(x) = (x + 3)(x - 1) cuts x axis when f(x) = 0
(x + 3)(x - 1) = 0
x = -3 , x = 1
This gives points (-3,0) and (1,0)

Cuts y axis when x = 0 ie at (0,-3)

Thus have points (-3,0),(-1, - 4),(0,-3) and (1,0) and curve can then be drawn

Question 2
f(x) = 3e^x
When x = 0, y = 3 x e° = 3 x 1 = 3 so curve passes thro` (0,3)
as x --> + infinity , y--> +infinity
as x--> - infinity , y---.> 0
Curve lies above x -axis and passes thro` (0,3)
Curve can then be drawn

Answer 2

simple. plug in x=0, get a y value. plug in x=1, get a y value. plug in x=2, get a y value. continue plugging in x values, and put the points on a graph until you obtain a good shape. then connect the dots! don't forget to try negative values for x, also.