i must sketch graph of these 2 functions
y=4log4x+1
y=e^3x
I am unsure how to find x and y intercepts for this problems could anyone please show me formula how to get coordinates to make this graph
$\displaystyle f(x)=4\log 4x+1,f9,\infty)\to\mathbf{R}$
To find the interecept with x-axis, you must to solve the equation $\displaystyle f(x)=0$.
$\displaystyle \displaystyle 4\log 4x+1=0\Rightarrow \log 4x=-\frac{1}{4}\Rightarrow 4x=10^{-\frac{1}{4}}\Rightarrow x=\frac{1}{4\cdot 10^{\frac{1}{4}}}$
The graph does not intercept y-axis.
$\displaystyle g(x)=e^{3x},g:\mathbf{R}\to(0,\infty)$
The graph does not intercept the x-axis.
To find the intercept with y-axis, you have to calculate $\displaystyle g(0)$:
$\displaystyle g(0)=1$
Then give to $\displaystyle x$ some other values in the domain to find some other values for $\displaystyle f$ or $\displaystyle g$.
Here are the sketches.