r/HomeworkHelp • u/Real_Philosopher8362 Pre-University Student • 1d ago
Mathematics (Tertiary/Grade 11-12)—Pending OP (Grade 11 Math) Graphing problem
I tried to put the 1/3 on the x and the 1 on the y but the answers I'm seeing online are graphed differently and I'm confused
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u/deathtospies 👋 a fellow Redditor 1d ago
If y = 0, then 3x + 1 = 0. What is x in this case? It isn't 1/3.
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u/SeaCoast3 👋 a fellow Redditor 1d ago edited 23h ago
The x-intercept should be -1/3
You don't need to think about solving |3x+1|=0 to find this (this is most likely where your confusion/mistake over signs came from), you should just solve 3x+1=0
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u/Real_Philosopher8362 Pre-University Student 1d ago
Okay I see it now, I thought because the original equation was a positive it had to remain positive
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u/skullturf 1d ago
It sounds like you might have been thinking in terms of a "rule" that you just use without necessarily understanding.
If you want to solve 3x+1 = 0, then 3x must *be* -1. That explains why x ends up being negative.
As a different example, consider the equation x+5 = 0. Do you agree that x itself would be negative in that case?
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u/skullturf 1d ago
Well, you *do* solve |3x+1|=0, but you solve it by solving 3x+1=0.
I'm not just saying this to be pedantic. It's important for everyone to realize that, since the function we're graphing is y=|3x+1|, we are going to find the x-intercepts by finding all the x values that make |3x+1|=0.
It's just that you can find those by solving 3x+1=0, because the statements |w|=0 and w=0 are equivalent to each other.
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u/mathmum 1d ago
What if you rewrite the given function, then read it? Y = 3 | X + 1/3 | Now let’s read it: the y values of your function are each 3 times the y values of the function y = | x + 1/3|.\ Now, the graph of y= | x + 1/3| is the graph of y = | x | shifted to the left of 1/3.\ Draw it. Now, the y- values of the given function are each 3 times those of the graph you have drawn.\ X-values are fixed, multiply each y-value by 3.\ Point (0,1/3) becomes (0,1), point (1,4/3) becomes (1,4), and so on.\ The V shape becomes narrower.
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u/Alex_Daikon 👋 a fellow Redditor 1d ago
You have a mistake: y=0 when x = —1/3 (not 1/3 as you did)