If you have ever swum in a pool and your eyes began to sting and turn red, you are aware of the effects on an incorrect pH level. The pH level measures the concentration of hydronium ions and can be modeled by the function p (t) = - log10 t. The variable t represents the amount of hydronium ions, and p (t) gives the resulting pH level.

Water at 25 degrees Celsius has a pH of 7. Anything that has a pH lower than 7 is called acidic, while pH's above 7 are basic or alkaline. Seawater has a pH just over 8, while lemonade has a pH of approximately 3.

1. Create a graph of the pH function. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.

The pH value is 1 at the orange dot, and is 1 at the red dot.

The transformation p (t+1) results in a y-intercept.

In this graph, the blue line is the original and first parent function p (t) = - log10 t. The pink line represent p (t) + 1, the transformation shifts up the y-axis by 1, but the p (t) + 1 transformation does not result in a y-intercept like the ones prior. The gold line represents p (t + 1), which shifts horizontally by 1 to the left. This does result in a y-intercept, because the graph doesn't completely flip over the line to the other side, and the green line represents - 1*p (t), which causes the graph to flip upside down, and doesn't end up as a y - intercept.