Mathematics Problems with Solutions | Desklib

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Question 1
Slope is given by y2-y1/x2-x1
=given the points (9,-2) and (7,2)
The slope = 2—2/7-2 = 4/-2 = -2
Question 2
Slope intercept equation
The line equation is given by y =mx + c
The slope , m = ¼
Pass point is given as (6, -3)
Therefore;
-3 = ¼ *6 + c
-3 = 3/2 + c
-3-3/2 =c
C = -9/4
Y= 1/4x -9/4
Question 3
The midpoint of segment is given by
M = ¿)

Given the two end points as (-5,6) and (-6,4)
= ¿ )
The midpoint = (-11/2, 5)
Question 4
Graph y = |x| + 3
The graph equation can be written as f(x) = -x+ 3
The function of f(-x) = x+ 3 = -(x-3) for –f(x)
Therefore f(x) ≠ f(-x)
This is an odd function meaning that the graph is symmetrical with the origin
Question 5
Domain of a function f(x) = 𝑓(𝑥) = (3𝑥−3)/ (𝑥 2−𝑥−2)
= (3𝑥−3)/ (𝑥 2−𝑥−2)= 3(x-1) (x – 2)(x + 1)
Question 6
The domain of the piecewise is -2 to 2 while the range is -1 to 3
Question 7
5x2- 2x =2 = 0 therefore a = 5, b=-2 and c =2
Using quadratic equation;
x=−b ± √b2−4 ac
2 a