StudentAidUnit 10: Unit 10 — Exercise 10 1
9th Class Mathematics · Unit 10: Unit 10
1.(i) Sketch the graph of y = 3x - 5 (ii) Sketch the graph of y = -2x + 8 (iii) Sketch the graph of y = 0.5x - 1
Given
(i) Function
y = 3x - 5
Working
Table of values
Points: (-1,-8), (0,-5), (1,-2), (2,1)
Given
(ii) Function
y = -2x + 8
Working
Table of values
Points: (-1,10), (0,8), (1,6), (2,4), (4,0)
Given
(iii) Function
y = 0.5x - 1
Working
Table of values
Points: (-2,-2), (-1,-1.5), (0,-1), (1,-0.5), (2,0), (3,0.5)
(i) Linear graph through pointsquad (ii) Linear graph through pointsquad (iii) Linear graph through points
2.(i) Sketch the graph of y = x³ + 2x² - 5x - 6 for -3.5 ≤ x ≤ 2.5 (ii) Sketch the graph of y = x² + x - 2 (iii) Sketch the graph of y = x³ + 3x² + 2x for -2.5 ≤ x ≤ 0.5 (iv) Sketch the graph of y = 5x² - 2x - 3
Given
(i) Function
y = x3 + 2x2 - 5x - 6
Working
Table of values
Selected points from x=2.5 to x=1
Given
(ii) Function
y = x2 + x - 2
Working
Table of values
Points: (-4,10), (-3,4), (-2,0), (-1,-2), (0,-2), (1,0), (2,4), (3,10)
Given
(iii) Function
y = x3 + 3x2 + 2x
Working
Table of values
Points from x=-2.5 to x=0.5
Given
(iv) Function
y = 5x2 - 2x - 3
Working
Table of values
Points: (-2,21), (-1,4), (0,-3), (0.5,-2.8), (1,0), (2,13)
(i) Cubic graphquad (ii) Parabolaquad (iii) Cubic graphquad (iv) Parabola
3.(i) Sketch the graph of y = 4^x (ii) Sketch the graph of y = 5^-x (iii) Sketch the graph of y = 1/(x-3) for x ≠ 3 (iv) Sketch the graph of y = 2/x + 3 for x ≠ 0 (v) Sketch the graph of y = x^(1/2) (square root) (vi) Sketch the graph of y = 3x^(1/3) (cube root) (vii) Sketch the graph of y = 2x^(-2) = 2/x²
Given
(i) Function
y = 4x
Working
Table of values
Points: (-2,0.06), (-1,0.25), (0,1), (0.5,2), (1,4), (1.5,8), (2,16), (2.5,32)
Given
(ii) Function
y = 5-x
Working
Table of values
Points: (-2.5,56), (-2,25), (-1,5), (0,1), (1,0.2), (2,0.04), (3,0.008)
Given
(iii) Function
y = 1x-3
Working
Table of values
Points with vertical asymptote at x=3
Given
(iv) Function
y = 2x + 3
Working
Table of values
Points with vertical asymptote at x=0, horizontal asymptote at y=3
Given
(v) Function
y = x1/2 = sqrt{x}
Working
Table of values
Points: (0,0), (1,1), (4,2), (9,3), (16,4), (25,5), (36,6)
Given
(vi) Function
y = 3x1/3 = 3sqrt[3]{x}
Working
Table of values
Points: (-4,-4.8), (-3,-4.3), (-2,-3.8), (-1,-3), (0,0), (1,3), (2,3.8), (3,4.3), (4,4.8)
Given
(vii) Function
y = 2x-2 = 2x2
Working
Table of values
Points: (-4,0.13), (-3,0.22), (-2,0.5), (-1,2), (1,2), (2,0.5), (3,0.22)
(i) Exponential graphquad (ii) Exponential decay graphquad (iii) Reciprocal function with asymptotequad (iv) Reciprocal function with asymptotesquad (v) Square root functionquad (vi) Cube root function scaled by 3quad (vii) Reciprocal squared function