which of the following is not a type of break in the graph?
a) holes
b) horizontal asymptotes
c) jumps
d) vertical asymptotes
I know for sure that a is not the answer and i doubt that c is the answer. I think the answer would be b.
2. Describe what can be inferred about the line tangent to a curve if the slope at a point is found to be 0?
I agree with your choice of b) for #1
If the slope of the tangent is zero, then the tangent must be a horizontal line and you are at either a maximum or a minimum point of the curve.
Ah, let's have some fun with these questions!
For the first one, let's see. We have holes, horizontal asymptotes, jumps, and vertical asymptotes. Now, out of all these options, the answer that's not a type of break in the graph is... drumroll, please... b) horizontal asymptotes! They don't result in any breaks or holes in the graph, but rather they serve as guide rails to assist the line.
Now, for the second question. If the slope at a point on a curve is found to be 0, it means the line tangent to that point is... wait for it... perfectly horizontal! Yep, I'm talking about a line that's as flat as a pancake. So, you can infer that there's no uphill or downhill action happening at that precise point. It's like the curve is taking a little rest and enjoying the horizontal view.
Hope that brings a smile to your face! Let me know if you need anything else.
The answer to the first question is indeed b) horizontal asymptotes. Holes, jumps, and vertical asymptotes are all types of breaks in the graph, while horizontal asymptotes are not breaks but rather describe the behavior of the graph at extreme values of x.
Regarding your second question, if the slope at a point on a curve is found to be 0, it can be inferred that the line tangent to the curve at that point is horizontal. A slope of 0 indicates that the tangent line is parallel to the x-axis, meaning it has no vertical component and is horizontal.
To determine which of the options is not a type of break in the graph, we can look at the characteristics of each option.
a) Holes: These are discontinuities in the graph where a point is missing, but the graph can still be connected by filling in the hole.
b) Horizontal asymptotes: These are lines that represent the behavior of the graph as x approaches positive or negative infinity. They do not indicate breaks in the graph.
c) Jumps: These occur when there is a sudden, non-continuous change in the graph at a particular x-value. They create a visible gap or jump in the graph.
d) Vertical asymptotes: These are lines that represent the behavior of the graph as x approaches a specific value. They occur when the graph approaches infinity or negative infinity at that point.
Based on the definitions provided, we can see that horizontal asymptotes (option b) do not indicate breaks in the graph. Therefore, the correct answer is b) horizontal asymptotes.
Regarding the second question, if the slope at a point on a curve is found to be 0, it means that the tangent line to the curve at that point is horizontal. This implies that there is no vertical change (rise) as we move along the tangent line, only horizontal change (run). In other words, the curve is not getting steeper or shallower at that specific point.