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7.07 Graphing Logarithmic Functions
Transcript of 7.07 Graphing Logarithmic Functions
A pool company forgets to bring their logarithmic charts, but they need to raise the amount of hydronium ions in a pool by 0.50. Using complete sentences, explain how your graph can be used to solve 10^-y = 0.50. Find the approximate solution.
The pool company has developed new chemicals that transform the pH scale. Using the pH function p(t) = –log10 t as the parent function, explain which transformation would result in a y-intercept. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
–1 • p(t)
The black line is the original parent function, p(t) = –log10 t. The red line is p(t) + 1, the transformation is shifting up the y-axis by 1, but it's not the y-intercept. The blue line is p(t +1), and it's shifting horizontally by 1 to the left and is the y-intercept. The green line is -1• p(t), this causes the graph to flip upside down.
Create a graph of the pH function. Locate on your graph where the pH value is 0 and where t is 1. You may need to zoom in on your graph.
The pH value is 1 on the x-axis.
The pH value is 3 on the y-axis
Parent (Black) : y = -log(t)
Graph 1 (Red) : y = -log(t) + 1
Graph 2 (Blue): y = -log(t + 1)
Graph 3 (Green) : y = -1 • -log(t)
The original function is y= -log10t and what you are looking to find is 10^-y=0.50. y=-log10t would then multiply both sides by -1 which will equal -y=10t. You can then use the log property to get 10^-y= t. Which would equal t= 0.50 and y=.03.