Question

Which function inputs will result in a horizontal stretch of the function f(x) = x? Check all that apply. F f(StartFraction 3 Over two EndFraction x) f(x + 2) f f(StartFraction one-half EndFraction x) f(x – 3.2) f(x) f f(StartFraction 2 Over 3 EndFraction x)

Answer 1

Answer:

The correct options are;

3) f(1/2·x)

5) f(2/3·x)

Step-by-step 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.