Describe the transformation that occurs when: g(x) = f(x) becomes g(x) = 8(f(x))

The graph will stretch vertically and horizontally

The graph will stretch vertically making it look thinner

The graph will not change

The graph will shrink vertically making it look fatter

Advance topics

The graph is being stretched vertically, so it will be thinner.

Step-by-step explanation:

g(x) = 8f(x) means that you are multiplying each original y-value by 8, so the graph gets thinner. When there's a number n greater than 1 in front of the function, it's a vertical stretch by n.

A. R2 = 0.6724, meaning 67.24% of the total variation in test scores can be explained by the least‑squares regression line.

Step-by-step explanation:

John is predicting test scores of students on the basis of their home work averages and he get the following regression equation

y=0.2 x +82.

Here, dependent variable y is the test scores and independent variable x is home averages because test scores are predicted on the basis of home work averages.

The coefficient of determination R² indicates the explained variability of dependent variable due to its linear relationship with independent variable.

We are given that correlation coefficient r= 0.82.

coefficient of determination R²=0.82²=0.6724 or 67.24%.

Thus, we can say that 67.24% of total variability in test scores is explained by its linear relationship with homework averages.

Also, we can say that, R2 = 0.6724, meaning 67.24% of the total variation in test scores can be explained by the least‑squares regression line.