Try the fastest way to create flashcards
Question

# Determine whether the graph of each function is symmetric with respect to the origin. $f(x)=5 x^{2}+6 x+9$

Solution

Verified
Step 1
1 of 2

To check for $\textbf{origin symmetry}$, we need to replace $x$ with $-x$ and $f(x)$ with $-f(x)$. If we get an equal expression, the function is $\textbf{symmetrical}$ in regards to the $\textbf{origin}$.

\begin{align*} f(x)&=5x^2+6x+9 \to -f(x)=5\left(-x\right)^2 -6x+9 \to -f(x)=5x^2 -6x +9\\ f(x)&\ne -5x^2+6x-9\\ \end{align*}

Since we did not get a valid expression, $f(x)$ is $\textbf{not symmetrical in regards to the origin}$.

## Recommended textbook solutions #### Precalculus

2nd EditionISBN: 9780076602186 (1 more)Carter, Cuevas, Day, Malloy
8,886 solutions #### Advanced Mathematical Concepts: Precalculus with Applications

1st EditionISBN: 9780078682278Carter, Cuevas, Holliday, Marks
7,568 solutions #### Nelson Functions 11

1st EditionISBN: 9780176332037Chris Kirkpatrick, Marian Small
1,275 solutions #### Precalculus with Limits

3rd EditionISBN: 9781133962885 (2 more)Larson
11,244 solutions