# Functions and Systems of Equations

> TSI Math Test Study Guide · Hightower High School P-TECH (2023)
>
> Source: [complete Markdown guide](../TSI-Math-Test-Study-Guide.md) · [original PDF](../1062198634-Hightower-TSI-Test-Study-Guide-v2-MATH.pdf)


#### 1. Which of the following could be the function shown below?

![Graph for question 1](assets/functions/q1-v-graph.jpg)

**A.** $f(x) = |x + 1|$

**B.** $f(x) = |x - 1|$

**C.** $f(x) = |x| + 1$

**D.** $f(x) = |x| - 1$


#### 2. What is the equation of the graph at the right?

![Graph for question 2](assets/functions/q2-parabola.jpg)

**E.** $y = (x - 2)^2 - 9$

**F.** $(x + 5)(x - 1) = 0$

**G.** $y = (x + 2)^2 - 9$

**H.** $(x - 5)(x + 1) = 0$

**I.** $y = x^2 + 4x + 5$


#### 3. Which of the following could be the graph of $y=-\sqrt{x}$?

![Graph choices for question 3](assets/functions/q3-graph-choices.png)

**A.** Upper-left graph

**B.** Lower-left graph

**C.** Upper-right graph

**D.** Lower-right graph


#### 4. In the $xy$-plane, the equation $y = x^2 + 2$ intersects the $x$-axis at how many points?

**J.** None

**K.** One

**L.** Two

**M.** Three


#### 5. What is the equation of the graph at the right?

![Graph for question 5](assets/functions/q5-square-root.jpg)

**A.** $f(x) = -\sqrt{x - 1}$

**B.** $f(x) = -\sqrt{x + 1}$

**C.** $f(x) = (x + 1)^2$

**D.** $f(x) = -(x - 1)^2$


#### 6. What is the equation of the graph at the right?

![Graph for question 6](assets/functions/q6-square-root.jpg)

**N.** $f(x) = \sqrt{x}$

**O.** $f(x) = - \sqrt{x}$

**P.** $f(x) = x^2$

**Q.** $f(x) = - x^2$


#### 7. What are the coordinates of the point of intersection of y = x + 3 and y = 3x − 3?

**A.** (2,5)

**B.** (3,6)

**C.** (4,9)

**D.** (5,12)


#### 8. How many solutions can the systems of linear equations below have? x + 4y = 3 2x + 8y = 4

**A.** None

**B.** One

**C.** Two

**D.** Infinite (∞)


#### 9. Jan bought 5 notebooks, Kim bought 4 notebooks and \$18.00 schoolbag. Together, Jan and Kim spent \$45.00. If each notebook costs the same, how much did each notebook cost?

**A.** \$3.00

**B.** \$3.50

**C.** \$4.50

**D.** \$5.00


#### 10. Margo bought 7 pens from a bookstore. Some of the pens cost \$3 each, and the rest cost \$4 each. If she paid a total of \$23 for the pens, how many of the \$3 pens did she buy?

**A.** Two

**B.** Three

**C.** Four

**D.** Five


#### 11. A group consisting of 10 children and adults went to a movie theater. Children’s tickets cost \$5 each and adult’s ticket cost \$8 each and the total cost for the 10 people was \$62. How many children were in the group?

**A.** 4

**B.** 5

**C.** 6

**D.** 7