Question

the domain of an exponential function is all real numbers. the range of an exponential function is positive real numbers. complete the graph of an exponential function has dropdown.

Explanation:

Step1: Recall exponential function graph properties

Exponential functions of the form \( y = b^x \) (where \( b>1 \)) have a horizontal asymptote. From the graph, we see the curve approaches the x - axis (y = 0) as \( x\to-\infty \), so it has a horizontal asymptote (y = 0 in this case). Also, exponential functions with \( b > 1 \) are increasing, and they have a y - intercept (when \( x = 0 \), \( y=b^0 = 1\), but in the given graph, when \( x = 0 \), \( y\) seems to be 1? Wait, the graph shown has a y - intercept and approaches the x - axis as \( x\) goes to the left. The key property here is that the graph of an exponential function (for \( b>1 \)) has a horizontal asymptote (y = 0), is increasing, and passes through (0,1) (in the standard form). But the question is about what the graph has. Common properties: a horizontal asymptote (since as \( x\to-\infty \), \( y\to0 \) for \( y = b^x,b > 1 \)), it's an increasing function (since \( b>1 \)), and a y - intercept. But the most characteristic feature related to the graph's structure is a horizontal asymptote (or we can say it has a horizontal asymptote, is increasing, etc. But from the context, the graph of \( y=b^x(b > 1) \) has a horizontal asymptote (y = 0), and it's a curve that rises from the horizontal asymptote (x - axis) as \( x\) increases, with a y - intercept at (0,1) (in the standard case). So the answer should be a horizontal asymptote (or we can say "a horizontal asymptote" or "an increasing curve" or "a y - intercept", but the main structural property is the horizontal asymptote. Wait, the question is "The graph of an exponential function has...", and for \( y = b^x,b>1 \), the graph has a horizontal asymptote (y = 0), is increasing, and passes through (0,1). But looking at the graph, it approaches the x - axis (horizontal line y = 0) as \( x\) goes to negative infinity, so it has a horizontal asymptote.

Step2: Determine the answer

From the graph of \( y=b^x(b > 1) \), we can see that as \( x\to-\infty \), the function approaches \( y = 0 \) (the x - axis), so the graph has a horizontal asymptote. Also, it's an increasing function. But the standard answer for the graph of \( y = b^x(b>1) \) is that it has a horizontal asymptote (y = 0), is increasing, and has a y - intercept at (0,1). But the question is asking what the graph has. So the correct completion is that the graph of an exponential function (with \( b>1 \)) has a horizontal asymptote (or "a horizontal asymptote", "an increasing curve", etc. But the most appropriate property here is a horizontal asymptote (since the graph approaches the x - axis as \( x\to-\infty \)).

Answer:

a horizontal asymptote (or "an increasing curve", or more precisely, for \( y = b^x(b>1) \), the graph has a horizontal asymptote (y = 0), is increasing, and has a y - intercept. But from the graph shown, the key feature is a horizontal asymptote (the x - axis) that the graph approaches as \( x\) decreases).