If f(x) is a continuous function defined for all real numbers, f(-1)=1, f(-5)=-10, and f(x)=0 for one and only one value of x, then which of the following could be that x value?
a) -6
b) -5
c) -4
d) 0
It's D.
You'll have to plot the given Points and see which could be possible value of x when f(x) is Zero.
Well, this question reminds me of a classic joke. Why was six afraid of seven? Because seven eight (ate) nine!
Now, let's get back to the problem at hand. We know that f(x) is continuous, which means there are no sudden jumps or breaks in the graph. So, if f(x) equals 0 at one point, it must cross the x-axis at that point.
We are given that f(-1) = 1, which indicates that the graph of f(x) is above the x-axis at x = -1. We are also given that f(-5) = -10, implying that the graph is below the x-axis at x = -5.
So, the graph starts above the x-axis at x = -1, goes below the x-axis at x = -5, and must come back up and cross the x-axis to hit f(x) = 0.
Looking at the options, we see that the only possibility is option c) -4. It's like finding the one missing piece to complete a puzzle!
To find the potential value of x that satisfies the given conditions, we need to analyze the information provided.
1. We know that f(x) is a continuous function defined for all real numbers. This means that there are no breaks or jumps in the graph of the function.
2. We are given that f(-1) = 1. This means that the function takes the value of 1 when x = -1.
3. We are also given that f(-5) = -10. This means that the function takes the value of -10 when x = -5.
4. Lastly, we know that f(x) = 0 for only one value of x. This implies that there is only one x-value at which the function crosses or touches the x-axis.
After analyzing this information, we can conclude that the only possible value for x is -5 (option b). This is because f(x) = 0 for one and only one value of x, and we already know that f(-5) = -10, which means that the graph of the function must cross the x-axis at x = -5.
To find the value of x for which f(x) equals 0, we need to consider the given information. We know that f(x) is continuous for all real numbers, meaning there are no breaks or jumps in the graph of the function.
We are also given three specific points on the graph of f(x): (-1, 1), (-5, -10), and the point where f(x) equals 0.
Let's evaluate each option to see which one could be the x value for f(x) = 0:
a) If x = -6, then f(-6) could be a possible x value. However, if f(-6) = 0, it would mean there's another value of x for which f(x) = 0, which is not allowed according to the given information.
b) If x = -5, then f(-5) could be the x value we are looking for. Since f(-5) = -10 and we know the function is continuous, there is a point where the graph crosses the x-axis, resulting in f(x) = 0. So, option b) is a potential solution.
c) If x = -4, then f(-4) could potentially be the correct x value. However, we do not have enough information to determine whether f(-4) = 0 or not, as it is not given in the question.
d) If x = 0, then f(0) could potentially be the correct x value. However, we do not have enough information to determine whether f(0) = 0 or not, as it is not given in the question.
Therefore, based on the given information, option b) -5 is the only choice that could be the x value for which f(x) = 0.