Question

which equation is represented by the graph below?

\\(y = e^x + 5\\)
\\(y = e^x + 4\\)
\\(y = \ln x + 4\\)
\\(y = \ln x + 5\\)

Explanation:

Identify key features of the graph

Using the Logarithmic Function Transformations knowledge point

• The graph has a vertical asymptote at \(x = 0\) (the y-axis).
• The curve passes through the point \((1, 4)\).
• The shape represents a logarithmic curve rather than an exponential curve.

Evaluate the given options at the key point

Using the Logarithmic Evaluation knowledge point

• For \(y = \ln x + 4\):

$$ y(1) = \ln(1) + 4 = 0 + 4 = 4 $$

• For \(y = \ln x + 5\):

$$ y(1) = \ln(1) + 5 = 0 + 5 = 5 $$

• The point \((1, 4)\) lies on the graph, which matches \(y = \ln x + 4\).

Answer:

• \(y = e^x + 5\)
• \(y = e^x + 4\)
• \(y = \ln x + 4\) (Correct answer)
• \(y = \ln x + 5\)