The x intercept is where the graph crosses the x axis.
In other words you need to find f(0)
Hi, I'm having some issues with this problem:
I need to solve for the x intercept of the graph of f.
I tried to do it like so:
That gives me: .2116484012
Using my graphing calculator to get the intersection of:
Gives an answer of: .21972246
Would someone mind explaining what I've done wrong? Thanks!
Yes f(0) = 4 which is the/an x-intercept which is what the question asked for
The y intercept is
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You went wrong between these two steps: and
You can't do that because the exponent is only on . For that to work you'd need the exponent on the 2 and the e. Instead you'd have to split the logs into
edit 2: You can use the change of base rule to see that
Ah, I see how I went wrong with my exponent not being attached to both terms. Thanks!
edit: However I'm still a bit confused on the x vs y intercepts. Putting my answers into the webwork form and using 4 as the y intercept and 2.1972246 as the x intercept came back as correct. I thought f(0) is the y intercept because the y intercept is where x=0 ? Conversely the x intercept would be where y = 0. Am I missing/forgetting something with that?
From what I gather you have the definition of intercept the wrong way around.
The x intercept is where the graph crosses or touches the x axis. Thus, by deifintion the x value of that point(s) must always be 0. On your graph this makes (0,4) a point.
The y intercept is where it crosses or touches the y axis and hence y=0 and you will have (x,0) which usually requires more effort to find.
To find the x-intercept you calculate and to find the y intercept you find . I hope that's clearer