Carcass wrote:
Attachment:
GRE The figure above shows the graph .jpg
The figure above shows the graph of the function h and line segment \(\overline{AB}\), which has a y-intercept of (0, b).
Quantity A |
Quantity B |
The number of values of x between j and k for which h(x) = b |
4 |
A lot of students will have trouble with the notation used here. So, let's examine that first.
First of all, every point on the curve satisfies the equation of that curve.
In this particular case, we aren't told what that equation is. All we know is that, y = h(x)
So, for example, if h(x) = 2x + 1, then the equation of the curve would be y = 2x + 1
If it were the case that h(x) = x² - 3x - 4, then the equation of the curve would be y = x² - 3x - 4
And so on.
Now let's say the point
(-3, 13) lies ON the curve.
This tell us that, when x = -3, y = 13
Since y = h(x), this means h(-3) = 13
In other words, when we plug x = -3 into the function, the output is 13
Let's also say the point
(5, 3) lies ON the curve.
This tell us that, when x = 5, y = 3
This means h(5) = 3
In other words, when we plug x = 5 into the function, the output is 3
Now let's move on to the question: How many values of x between j and k are there for which h(x) = b?
Since y = h(x), we can reword the question as follows: How many values of x between j and k are there for which y = b?
In other words, how many points lie on the curve such that the y-coordinate is b?
We've already been told that the LINE AB intersects the y-axis at the point (0,b)
If we draw a horizontal line from this point, all of the points on this horizontal line will have
b as their y-coordinate
We can all see that there are THREE points on the curve that have
b as their y-coordinate
In other words, there are THREE x-values that such that h(x) = 3
We get:
Quantity A: 3
Quantity B: 4
Answer: B