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For Q8(a)(ii), I don't understand how you get the range of x-values. Mind if you can explain how to get x <=2.5 and further how to find the range of m?
X = 2.5 is where the modulus function has the v-shaped vertex, as you can see from the sketch I drew. When m = -2, the line y = -2x + 3 is parallel to the modulus line for values of x < 2.5. Hence, for the graph to cut twice, the line y = mx + 3 is valid for gradient values of -2 or greater ( m > -2). Made a noob mistake on the gradient.
The Question 8(a)(ii) ask for two point intersection, so isn't the value of m also positive and negative at the same time for the range of m?
Not necessarily. Range just means more than one possible value. If m is less than -2, (say -3, -4, or more negative, it will cut the modulus function only once. Try sketching these lines to better understand. Note that all these lines pass through the point (0,3).
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Better illustration. Brain half dead during the holidays.. lol
Date Posted:
5 years ago