Sketch the Graph of h(x) = 8 + log_2(x) in MyMathlab

TL;DR

Learn how to graph a logarithmic function by shifting it vertically and identifying asymptotes.

Transcript

hi everyone in this video we have to graph the function H of x equals 8 plus log base 2 of X so if you were just graphing log base 2 of X the idea is that we have this memorized so it has a vertical asymptote at 0 and it looks like this so you want to have that memorized so whenever you're doing one of these graphing problems you want to start with... Read More

Key Insights

• 🚦 Logarithmic functions have a vertical asymptote at x=0.
• 📈 Adding a value to the logarithm shifts the graph up or down.
• ❓ Domain of logarithmic functions starts from the asymptote.
• 🧡 Range for log functions covers all real numbers.
• 😀 Vertical shifts in logarithmic functions only affect the y-axis.
• 📈 Identifying and plotting asymptotes is crucial in graphing logarithmic functions.
• ❓ Logarithmic functions exhibit unique characteristics in graphing.

Questions & Answers

Q: How does adding a value to the logarithm affect the graph?

Adding a value to the logarithm shifts the graph vertically; adding a positive value moves it up, negative value moves it down, left for subtraction and right for addition.

Q: Why is the vertical asymptote at 0 for log base 2 of X?

The vertical asymptote at 0 is due to the nature of the logarithmic function, where the base determines the behavior of the graph.

Q: Why is the domain for logarithmic functions defined as it is?

The domain of a logarithmic function starts at the vertical asymptote since log functions are not defined for non-positive numbers, hence starting from zero.

Q: How does shifting the graph vertically affect the domain and range?

Shifting the graph vertically does not influence the domain but affects the range, which remains all real numbers for logarithmic functions.

Summary & Key Takeaways

• Graphing a function with log base 2 of X involves starting with a vertical asymptote at 0.

• Adding a value to the logarithm shifts the graph vertically accordingly.

• The domain starts at the asymptote and the range covers all real numbers.