Graph g(x) = log_5(x + 3) with the MyMathlab Graphing Tool

TL;DR

Shift and graph a logarithmic function with a base of 5 by adding 3 to the x-values, adjusting the vertical asymptote and range accordingly.

Transcript

hi everyone in this video we have to graph the function G of x equals log base 5 of X plus 3 so whenever we're graphing a log function you first want to think about like the core function or the base function so what I mean by that is you want to think about just the graph of log X so the graph of log always has a vertical asymptote x equals 0 that... Read More

Key Insights

• ☺️ The logarithmic base function has a vertical asymptote at x = 0 and passes through (1,0).
• ☺️ Shifting a logarithmic function left involves adding a negative constant to the x-values for proper graph placement.
• 🧡 MathLab can be used to graph logarithmic functions, adjusting asymptotes and ranges accordingly.
• ❓ The domain of a graphed logarithmic function starts at the value it was shifted to, indicated in parentheses due to excluded values.
• 🧡 The range of a logarithmic function covers all real numbers, slowly increasing towards positive infinity.
• 📈 Understanding the impact of shifting on the graph helps accurately depict logarithmic functions.
• 🔨 Using appropriate tools like MathLab is essential for accurately visualizing adjusted mathematical functions.

Questions & Answers

Q: How does adding a constant to the x-values affect the graph of a logarithmic function?

Adding a constant to the x-values in a logarithmic function shifts the graph horizontally; in this case, adding 3 to x shifted the function 3 units to the left.

Q: Why is the vertical asymptote of G(x) equal to x = -3?

The vertical asymptote is at x = -3 because the function was shifted left by 3 units, reflecting the shift in the vertical asymptote.

Q: What is the domain of the graphed logarithmic function?

The domain starts at x = -3 and extends to positive infinity, written as (-3, ∞) due to the exclusion of -3 because of the vertical asymptote.

Q: Why is the range of a logarithmic function from negative to positive infinity?

The range of a logarithmic function covers all real numbers due to the slow increase towards infinity, despite appearing to approach a limit, resulting in the range from -∞ to ∞.

Summary & Key Takeaways

• Understanding the base log function with a vertical asymptote at x = 0 and passing through (1,0).

• Shifting the graph left by 3 by adding 3 to the x-values.

• Using MathLab to graph the shifted logarithmic function with the correct asymptote and range.