Bunuel wrote:
The function g has the property that g(a) = g(b) for all real numbers a and b. What is the graph of y = g(x) in the xy-plane?
A. A parabola symmetric about the 𝑥-axis
B. A line with slope 0
C. A line with slope 1
D. A line with no slope
E. A semicircle centered at the origin
GivenThe value of g(a) and the value of g(b) is same, and we know that for any two values in the space the value will be same. Hence we can infer that the output of the function f(x) does not depend on its input (i.e. x) and the function will provide a constant output throughout regardless of x.
A quick glance at the option tells is that it could possibly be B. However, let's use the process of elimination.
A. A parabola symmetric about the 𝑥-axisy = \(x^2\)
The value of y depends on the value of x. Hence this can be ruled out.
B. A line with slope 0y = mx + c, as m = 0
y = c
The value of y does not depend on x.
Hence, lets keep this.
C. A line with slope 1y = mx + c
y = x + c (as m = 1)
So the value of y depends on the value of x. We can eliminate this.
D. A line with no slopeThis means the line is parallel to y axis (I guess
) . We don't even have two points to consider for this line. So we can eliminate this
E. A semicircle centered at the originAgain the function of y will depend on x. Hence we can eliminate this.
IMO B