Problem 78

Question

The graph of $y=f(x)$ passes through the points $(0,1),(1,2),$ and $(2,3) .$ Find the corresponding points on the graph of $y=f(x+2)-1$.

Step-by-Step Solution

Verified

Answer

The corresponding points on the graph of $f(x+2) - 1$ will be $(-2, 0), (-1, 1), (0, 2)$.

1Step 1: Shifting the x-coordinate

This step involves moving the x-coordinates to left by 2 units. Hence, if a point on $f(x)$ is $(a, b)$, its corresponding point on the graph of $f(x+2) - 1$ will have x-coordinate $a - 2$. So the points $(0, 1), (1, 2), (2, 3)$ on $f(x)$ will be transformed to $(-2, 1), (-1, 2), (0, 3)$ respectively on $f(x+2) - 1$.

2Step 2: Shifting the y-coordinate

The final step is to shift these new points down by 1 unit. So, if a point on the graph of $f(x+2)$ is $(a, b)$, then its corresponding point on $f(x+2)-1$ will have y-coordinate $b - 1$. Thus, $(-2, 1), (-1, 2), (0, 3)$ will be shifted down to $(-2, 0), (-1, 1), (0, 2)$ respectively.

Problem 77

Problem 78

Other exercises in this chapter

Problem 77

Find two functions $f$ and $g$ such that $(f \circ g)(x)=h(x)$ (There are many correct answers.) $$h(x)=(x+4)^{2}+2(x+4)$$

View solution

Problem 77

A company produces a product for which the variable cost is $\$ 68.75$ per unit and the fixed costs are $\$ 248,000 .$ The product sells for $\$ 99.99 .$

View solution

Problem 78

Find the inverse function of $f$ algebraically. Use a graphing utility to graph both $f$ and $f^{-1}$ in the same viewing window. Describe the relationshi

View solution

Problem 78

The table shows the revenue $y$ (in thousands of dollars) of a landscaping business for each month of 2015, with $x=1$ representing January. $$\begin{array}

View solution