Question

function \\(y = b^x\\) (\\(b > 1\\))

the domain of an exponential function is all real numbers. the range of an exponential function is positive real numbers.

the graph of an exponential function has a y-intercept only.

the graph is dropdown: constant / decreasing / increasing throughout its domain and has dropdown the x-axis because the value \\(b^x\\) dropdown ose to 0 but never reach it.

Explanation:

Analyze the function behavior

Using the Exponential Function Graphs knowledge point
The given function is \(y = b^x\) where \(b > 1\). As \(x\) increases, \(b^x\) grows larger, meaning the function is increasing throughout its domain.

Determine the horizontal asymptote behavior

Using the Exponential Function Graphs knowledge point
As \(x \to -\infty\), \(b^x \to 0\). This means the graph has a horizontal asymptote at the \(x\)-axis (\(y = 0\)) because the value of \(b^x\) gets closer to \(0\) but never reaches it.

Answer:

The graph is <blank>increasing</blank> throughout its domain and has <blank>a horizontal asymptote at</blank> the \(x\)-axis because the value \(b^x\) gets very close to 0 but never reach it.