Could someone help me in this problem: I have a nondecreasing function $f(x)$ on $\mathbb R$ (so we know how the graph will looks like). How can we graph the functions $ax$, $f(x)$, and $ax+f(x)$, ($a>0$) all on the same $xy-$coordinate; which one is above the other?
Graph of $ax+f(x)$
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calculus
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0Well, you are asking which one is bigger $f(x)$ or $f(x)+ax$... What do you think? If to $f(x)$ you add a number, when does it become larger and when does it become less? – 2012-01-28
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0$ax+f(x)$ will be above $f(x)$ when $x>0$, equal to $f(x)$ when $x=0$, and below $f(x)$ when $x<0$. Without knowing more about $a$ and $f$, you can't say any more about which ones will be above or below the others. – 2012-01-28
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0I'm interested in $a=4$. – 2012-01-28