Question

how do you see it? the graphs of three functions are shown. which function(s) has real zeros? imaginary zeros? explain your reasoning. function f has, because its graph. function g has, because its graph. function h has, because its graph.

Explanation:

Step1: Recall zero - concept

The real zeros of a function are the \(x\) - values where the graph of the function intersects the \(x\) - axis. Imaginary zeros occur when the graph does not intersect the \(x\) - axis.

Step2: Analyze function \(f\)

The graph of function \(f\) intersects the \(x\) - axis. So, it has real zeros. Since it intersects the \(x\) - axis, it does not have only imaginary zeros.

Step3: Analyze function \(g\)

The graph of function \(g\) does not intersect the \(x\) - axis. So, it has imaginary zeros and no real zeros.

Step4: Analyze function \(h\)

The graph of function \(h\) intersects the \(x\) - axis. So, it has real zeros. Since it intersects the \(x\) - axis, it does not have only imaginary zeros.

Answer:

Function \(f\) has real zeros, because its graph intersects the \(x\) - axis.
Function \(g\) has imaginary zeros, because its graph does not intersect the \(x\) - axis.
Function \(h\) has real zeros, because its graph intersects the \(x\) - axis.