Answer:
The correct options are;
3) f(1/2·x)
5) f(2/3·x)
Explanation:
The given parameter is presented here as follows;
f(x) = x
Therefore;
f(x) = y = x
Comparing with the general equation for a straight line, y = m·x + c, we have;
For y = x, m = 1
∴ The slope = 1
1) For f(3/2·x) = y = 3/2·x, the slope, m = 3/2 which is a steeper slope than m=1 and therefore a has more increase in y than in x values or has a vertical stretch rather than a horizontal stretch
2) For f(x + 2) = y = x + 2, the slope, m = 1 which gives an equal slope of m = 1 to the slope in the question, f(x) = x, resulting in no change in stretch
3) For f(1/2·x) = y = 1/2·x, the slope, m = 1/2 which is a gentler slope slope than m=1 as y increase half unit, for each unit increase in x and the function is horizontally stretched
4) For f(x - 3/2) = y = x - 3/2, the slope, m = 1 which gives an equal slope of m = 1 to the slope in the question, f(x) = x, resulting in no change in stretch
5) For f(2/3·x) = y = 2/3·x, the slope, m = 2/3 which is a gentler slope slope than m = 1 as y increase 2/3 unit, for each unit increase in x and the function is horizontally stretched.