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/Tag: Functions
11 03, 2019

## Absolute Functions

Absolute Functions Go to the Forum to see more questions or ask your own Worked examples Consider the function $f(x) = x + |x|$ for –2 ≤ x ≤  2. Sketch the graph of $y=f(x)$ showing the endpoints. The best way to approach any graph where x is added to an absolute [...]

29 07, 2018

## Oblique Asymptotes

Oblique Asymptotes Worked Examples Sketch the graph of $y=\frac{{{x^2}}}{{x - 1}}$ , showing all the important features. Domain: all real x, x ≠ 1 we have a vertical asymptote at x = 1 Find the intercepts: at x = 0, y = 0 hence passes through the [...]

30 11, 2016

## Translations

By |2016-11-30T09:41:19+10:00November 30th, 2016|Tags: , , |Comments Off on Translations

Translations worked examples The function $f(x)$ is translated 7 units to the left and 4 units down. Which of the following equations represents the translated function? a. $f(x)=(x-7)^2-4$ b. $f(x)=(x-4)^2+7$ c. $f(x)=(x+7)^2-4$ d. $f(x)=(x-4)^2-7$ C $f(x)=(x+7)^2-4$ to move a graph up or down, we need to add/subtract [...]

24 11, 2016

## Vertical Asymptote

Vertical Asymptote worked examples Write the equation of the vertical asymptote of $y = \frac{x}{{2(1 - x)}}$.  2(1 - x) = 0 1 - x = 0 x = 1 to find the vertical asymptote, we need to find the value for which the function is undefined, which is [...]

26 10, 2016

## Discriminant

By |2016-10-26T18:35:14+10:00October 26th, 2016||Comments Off on Discriminant

Discriminant $\Delta=b^2-4ac$ Δ < 0 - no solutions Δ = 0 - one solution Δ > 0 - two solutions where y = ax2 + bx + c worked examples How many solutions does the equation: y = x2 + 4x + 8 = 0 have? Δ = 42 - 4 × 1 × [...]

26 10, 2016

## Circles

By |2016-10-26T16:45:32+10:00October 26th, 2016|Tags: , , |Comments Off on Circles

Circles x2 + y2 = r2 Centre (0, 0) Radius = r units Domain: -r ≤ x ≤ r Range: -r ≤ y ≤ r worked examples For the circle with equation x2 + y2 = 16, find: a. the centre b. the radius c. the domain [...]

16 10, 2016

## Parabola Worded Problems

By |2016-10-21T13:16:58+10:00October 16th, 2016||Comments Off on Parabola Worded Problems

Parabola Worded Problems worked examples A 20cm piece of wire is bent to form a rectangle. Let x cm be the breadth of the rectangle. a. Use the perimeter to to write an expression for the length of the rectangle in terms of x. b. Write an equation [...]

16 10, 2016

## Vertex Of Parabola

By |2016-10-26T18:25:46+10:00October 16th, 2016||Comments Off on Vertex Of Parabola

Vertex Of Parabola $x=-\frac{b}{2a}$ substitute x to find y if a > 0 concave up ∴ minimum if a < 0 concave down ∴ maximum where y = ax2 + bx + c worked examples Find the vertex of the parabola: y = x2 + 4x + 8. $x=-\frac{4}{2\times1}$ using $x=-\frac{b}{2a}$ where a = [...]

12 10, 2016

## Parabola Axis Of Symmetry

By |2016-10-26T15:16:42+10:00October 12th, 2016||Comments Off on Parabola Axis Of Symmetry

Parabola Axis Of Symmetry $x=-\frac{b}{2a}$ where y = ax2 + bx + c worked examples Find the axis of symmetry of the parabola: y = x2 + 4x + 8. $x=-\frac{4}{2\times1}$ using $x=-\frac{b}{2a}$ where a = 1, b = 4 and c = 8 substitute $x=-\frac42$ x = -2 simplify [...]

18 06, 2016

## Exponential

By |2016-10-21T13:17:02+10:00June 18th, 2016||Comments Off on Exponential

Exponential $y=2^x$ $y=2^{-x}$ worked examples On the same axis, draw the graphs of y = 2x, y = 3x and y = 4x.   We need to consider how changing the base number in front of affects the graph. Changing the number in the base has very [...]