Question

Sketch the graph of the function \(y = {10^{x + 2}}\) by using transformations if needed.

Short answer

The \(y\) intercept of \(y = {10^x}\) is observed to be \(1\).

Step-by-step solution

Given data

The function is\(y = {10^{x + 2}}\).

Concept of Vertical and horizontal shifts

Vertical and horizontal shifts:

When\(y = f(x) + c\)and\(c > 0\), shift the graph of\(y = f(x)\)a distance\(c\)units upwards.

When\(y = f(x) - c\)and\(c > 0\), shift the graph of\(y = f(x)\)a distance\(c\)units downwards.

When\(y = f(x) - c\)and\(c > 0\), shift the graph of\(y = f(x)\)a distance\(c\)units towards the right.

When\(y = f(x) + c\)and\(c > 0\), shift the graph of\(y = f(x)\)a distance\(c\)units towards the left.

Sketch the graph of the function \(y = {10^{x + 2}}\)

The standard graph of the function \(y = {10^x}\) is roughly sketched in figure 1 as follows

Figure 1

Then, to draw the graph of \(y = {10^{x + 2}}\), shift the graph \(y = {10^x}\) two units to the left.

Thus, the graph of \(y = {10^{x + 2}}\) is shown in figure 2 as follows:

Figure-2

From figure 2, the \(y\) intercept of \(y = {10^x}\) is observed to be \(1\).