MATH 107 Coursework Paper: Show Work for All Problems

SHOW WORK FOR ALL PROBLEMS
1 Consider the function: fx=-x2-1
* Find the x-intercepts
The Quadratic equation is used in calculating the x intercept and set f(x)=0
X=-b±√b2-4ac/ 2a
X=-0 ± √0-4/ -2
Alternatively setting F(x) = 0
Then =-x2-1
The equation has complex roots and no x intercept
* Find the y-intercepts
Substituting x for 0, then f (0) = - (0)2 – 1= -1, and hence the y intercept is (0,-1)
* Graph the function fx=-x2-1
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2 Consider the function:
fx=2 x<0x+1 0≤x≤5-2 5
* Sketch f(x)












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* Which intervals is f(x) increasing? Use interval notations.
F is increasing at x if f(x)>0
F(x) = 2 for x<0 and interval notation (∞, 0)
F (x) = x+1 for 0 ≤x≤5 and interval notation (0, 5)
* Which intervals is f(x) decreasing? Use interval notations.
F is decreasing at x if f(x) <0
F(x) = -2 for 5
3 Consider th...