Graphs of exponential functions and logarithmic functions provide a visual insight into their properties, such as growth, decay, and the inverse relationship between them. Graphs of exponential ...

A translation is a movement of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. The graph of \(y = f(x)\) where \(f(x) = x^2\) is the same as the ...

A translation is a shift of the graph either horizontally parallel to the \(x\)-axis or vertically parallel to the \(y\)-axis. If \(f(x) = x^2\), then \(f(x) + a = x^2 + a\). The value of \(a\) ...

A function is a relation such that for each \(x\)-value there is only one corresponding \(y\)-value. In other words, a function cannot contain two different ordered pairs with the same first ...