Mathematics

Problem

Consider the following four algebraic rules of real-valued relations: A.

y=|x|

y=x^{2}

y=x

y=\sqrt{x},\;x\ge 0

Four graphs, labelled P, Q, R and S, are described below. P. A straight line through the origin making an angle of

45^{\circ}

with the positive

x

–axis. Q. A V-shaped curve with vertex at the origin and both arms opening upwards. R. A U-shaped curve with vertex at the origin and opening upwards. S. A smooth curve passing through

(0,0)

and

(1,1)

, lying entirely in the first quadrant and rising more slowly as

x

increases. Answer the following: a. (i) Match each algebraic rule A–D with exactly one graph description P–S. b. (ii) For every matched pair, write the

x

-intercept(s), the

y

-intercept(s) and state whether the graph is symmetric about the

y

-axis. c. (iii) Give a brief reason for ONE of your matches in part (i) based on the shape or symmetry of the graph.

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