Draw the graph of the function `f(x) = max. {x, x^(2)}` and write its equivalent definition.

Explanation

To write the equivalent definition of the funcion, first draw the graph of `y=x and y= x^(2)`
Now from the graph, we can see that

for ` x in (-oo, 0)`, the graph of `y= x^(2)` lies above the graph of `y=x or x^(2) gt x`
for `x in (0, 1)`, the graph of y = x lies above the graph of `y= x^(2) or x gt x^(2)`
for `x in ( 1, oo)`, the graph of `y= x^(2) ` lies above the graph of `y = x or x^(2) gt x `
Hence we have `f(x) = {{:( x^(2)",",, x lt 0),( x",",, 0 le x le 1),( x^(2)",",, x gt 0):}`
For `f(x) = min. {x, x^(2)}`, we have `f(x) = {{:( x",",, x lt 0), ( x^(2)",",, 0 le x le 1),(x",",, x gt 0):}`