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Term 3 : Unit 5 Standard Graphs

Term 3 : Unit 5 Standard Graphs. 5.1 The Curves y = ax n and y 2 = kx. 5.2 The Curves of y = a x (a > 1) , y = a -x (a > 1), y = lg x and y = lnx. Name : __________( ) Class : ______ Date :_________. Standard Graphs.

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Term 3 : Unit 5 Standard Graphs

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  1. Term 3 : Unit 5Standard Graphs 5.1 The Curves y = axn and y2 = kx. 5.2 The Curves of y = ax (a > 1) ,y = a-x (a > 1), y = lg xand y = lnx Name : __________( ) Class : ______ Date :_________

  2. Standard Graphs 5.2 The Curves of y = ax (a > 1) ,y = a-x (a > 1), y = lg xand y = lnx Objectives • In this lesson, you will learn to • recognise the graphs of y = ax (a > 1) ,y = a-x (a > 1), y = lg xand y = lnx • and their properties,

  3. Standard Graphs Graphs of y = axn for n = –2, –1, 0, 1, 2, 3 For even powers of x, the graphs are symmetrical about the y-axis. For odd powers of x, the graphs are symmetrical about the origin. The basic shape stays the same as the value of a changes. a = 1 a = 3 a = 0.5 a = –1

  4. Standard Graphs Graphs of y = axn where n is rational For even powers of x, the graphs are defined for x ≥0 For odd powers of x, the graphs are defined for all values of x

  5. Standard Graphs Graphs of y2 = kx where k is a constant The curves are symmetrical about the x–axis.

  6. The line y = 2x + 1 intersects the x–axis at the point M and the curve at the points A and B. Standard Graphs Example 1: (a) Find the coordinates of A and of B. At the points A and B: Equate the two curves. Multiply throughout by x. (b) Find the ratio AM : MB. Substitute into y = 2x + 1. By similar triangles At M 2x + 1 = 0 Using x coordinates

  7. Standard Graphs Example 2: The line y = 2 – x intersects the curve y2 = 12 – 2x at the points A and B. (a) Find the coordinates of A and B. At the points A and B: Substitute for y in y2. (b) Find the perpendicular bisector of AB. Substitute into y = 2 –x. Using the midpoint formula. Gradient of perpendicular bisector = 1

  8. Standard Graphs 5.2 The Curves y = axn and y2 = kx Objectives • In this lesson, you will learn to • recognise the graphs of y = axn and y2 = kx and their properties, • find the intersection of a curve and a straight line.

  9. Standard Graphs

  10. y=ax y=ax y=logbx y=logbx Standard Graphs

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